https://icme.hpc.msstate.edu/mediawiki/api.php?action=feedcontributions&user=Burcham&feedformat=atomEVOCD - User contributions [en]2020-02-21T23:30:54ZUser contributionsMediaWiki 1.19.1https://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T20:55:05Z<p>Burcham: /* Geomaterials */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|400px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects showing interacting stress fields. From [[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model | this study]]]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
Finally, to garner more information about the information bridges between length scales go to the [[Mississippi State University| MSU Education page]].<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
*[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
*[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on the campus of Mississippi State University at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Biomaterials==<br />
<br />
== Ceramics==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
* [[M Scale Cement|Multiscale Modeling of Concrete]]<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T19:40:44Z<p>Burcham: /* Mesoscale Research */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
Finally, to garner more information about the information bridges between length scales go to the [[Mississippi State University| MSU Education page]].<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
*[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
*[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on the campus of Mississippi State University at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Biomaterials==<br />
<br />
== Ceramics==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T18:05:28Z<p>Burcham: /* Material Texture */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
*[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
*[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on the campus of Mississippi State University at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T18:03:12Z<p>Burcham: /* Material Texture */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
*[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
*[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at Mississippi State University at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T18:02:06Z<p>Burcham: /* Los Alamos Polycrystal Plasticity (LAPP) */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
*[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
*[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T18:01:18Z<p>Burcham: /* Dream 3D */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
*[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T18:00:55Z<p>Burcham: /* Microstructure Builder */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
*[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:59:41Z<p>Burcham: /* Microstructure Builder */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
Constructs simulated 3D polycrystalline materials, where the input is typically grain size and shape data. <br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:46:33Z<p>Burcham: /* Metals */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# [[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC model]] for polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:44:33Z<p>Burcham: /* Metals */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== Thermoplastic Internal State Variable (TPISV) Model ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element tension for Polycarbonate (ABAQUS-Explicit) -[[Media:OE_Tension.zip | here]]<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
In metals, mesoscale implies crystal plasticity. Crystal plasticity is a continuum theory, but it has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:33:15Z<p>Burcham: /* Abaqus CPFEM */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
===Abaqus Crystal Plasticity Finite Element Model (CPFEM)===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:31:33Z<p>Burcham: /* Visco-Plastic Self-Consistent (VPSC) */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum | VPSC Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:30:47Z<p>Burcham: /* Viscoplastic Self-Consistent */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
===Visco-Plastic Self-Consistent (VPSC)===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:28:22Z<p>Burcham: /* Polymers */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPGui User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:27:58Z<p>Burcham: /* Polymers */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co User Manual]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui Tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:24:51Z<p>Burcham: /* Metals */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in the [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in [[Thermoplastic Modeling|ABAQUS Explicit]] using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:20:39Z<p>Burcham: /* Metals */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
==Material Texture==<br />
Texture can be defined as a measure of the percentage of grains that are oriented with respect to a certain plane. The texture of a material is highly dependent upon the processing conditons. X-ray Diffraction is a viable technique that allows us to determine the initial and deformed bulk texture of a material being studied. The texture can be evaluated using [[Rigaku SmartLab X-ray Diffraction System]], which is available on-campus at the Institute for Imaging & Analytical Technologies (I2AT).<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]]<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:17:07Z<p>Burcham: /* = */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt Tutorial]<br />
<br />
===Dream 3D===<br />
3D reconstruction tool<br />
[http://dream3d.bluequartz.net/ Dream.3D website]<br />
<br />
===Microstructure Builder===<br />
[https://code.google.com/archive/p/mbuilder/ Simulated 3D polycrystalline material creator]<br />
<br />
<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:11:32Z<p>Burcham: /* MATLAB */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
[[MATLAB_Tutorials | MATLAB Tutorials]]<br />
* [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
* [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
* [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
* [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
* [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
* [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
* [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
* [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
* [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
* [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
* [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt | Tutorial]<br />
<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:06:00Z<p>Burcham: /* Viscoplastic Self-Consistent */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Viscoplastic Self-Consistent===<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt | Tutorial]<br />
<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T17:05:37Z<p>Burcham: /* Viscoplastic Self-Consistent */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===Plasticity-Damage (DMG) v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
==Viscoplastic Self-Consistent==<br />
[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
<br />
===Los Alamos Polycrystal Plasticity (LAPP)===<br />
Texture code that quantifies pole figures<br />
<br />
by Fred Cox: LANL<br />
<br />
[http://pajarito.materials.cmu.edu/rollett/27750/L12-LApp_tour_Aniso2-1Oct09.ppt | Tutorial]<br />
<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:56:03Z<p>Burcham: /* Concrete */</p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
Phase field method is a power computational tool to model the temporal and spatial evolution of microstructure in mesoscale region. Most materials have a complex microstructure that arise due to grain, grain boundaries, different phases, compositions, orientations and crystallography. The material properties can be improved if we could understand the evolution of the microstructure.<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
===Acrylonitrile Butadeine Styrene (ABS)===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
===Polycarbonate (PC) ===<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:21:41Z<p>Burcham: </p>
<hr />
<div><br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* One element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:17:49Z<p>Burcham: /* Material Models */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
* one element compression for polymer (ABAQUS-Implicit) -here<br />
* one element compression for aluminum A356 (ABAQUS-Explicit) -here<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:16:17Z<p>Burcham: /* MATLAB */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
===MATLAB===<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:15:02Z<p>Burcham: /* Abaqus CPFEM */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
MSU TPISV a damage model that is implemented into a glassy, amorphous thermoplastic thermomechanical inelastic internal state variable framework. Internal state variable evolution equations are defined through thermodynamics, kinematics, and kinetics for isotropic damage arising from two different inclusion types: pores and particles. The damage arising from the particles and crazing is accounted for by three processes of damage: nucleation, growth, and coalescence. Nucleation is defined as the number density of voids/crazes with an associated internal state variable rate equation and is a function of stress state, molecular weight, fracture toughness, particle size, particle volume fraction, temperature, and strain rate. The damage growth is based upon a single void growing as an internal state variable rate equation that is a function of stress state, rate sensitivity, and strain rate. The coalescence internal state variable rate equation is an interactive term between voids and crazes and is a function of the nearest neighbor distance of voids/crazes and size of voids/crazes, temperature, and strain rate. The damage arising from the pre-existing voids employs the Cocks–Ashby void growth rule. The total damage progression is a summation of the damage volume fraction arising from particles and pores and subsequent crazing. The modeling results compare well to experimental findings garnered from the literature. Finally, this formulation can be readily implemented into a finite element analysis.<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
'''Input files using CPFEM for an aluminum simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
'''Input files using CPFEM for a magnesium simulation'''<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
==MATLAB==<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Code:_ABAQUS_CPFEMCode: ABAQUS CPFEM2016-03-14T16:12:25Z<p>Burcham: /* Crystal Plasticity FEM Models */</p>
<hr />
<div>== Crystal Plasticity Finite Element Method ==<br />
<br />
CPFEM is based on a crystal plasticity constitutive model incorporated in the UMAT user subroutine of the commercial finite element software ABAQUS 6.9. The single crystal or polycrystal of face-centered cubic (FCC), body-centered cubic (BCC) and hexagonal closed (HCP) structures will respond to an applied stress by dislocation slip which is simulated using CPFEM. Orientations of grains will rotate during deformation. At the same time, the threshold stress of each slip systems will increase because of the self-hardening and latent hardening of the deformation modes. As such, the mechanical response (stress-strain curve) and the orientation of the crystals (texture) will be captured by the CPFEM. By comparing predicted results with experiments, one can get useful information about deformation mode activation, stress-strain data and crystal re-orientations, aspects that lead to a fundamentally understanding of the nature of metal deformation at the grain scale.<br />
<br />
* [[Media:Introduction_to_Crystal_Plasticity_Finite_Element_Method_v3.pdf| Introduction to Crystal Plasticity Finite Element Method (PDF file)]]. <br />
<br />
* (CAVS users only): [[cpfem decks| sources of the examples]] given in the introduction.<br />
<br />
== Introduction to CPFEM ==<br />
<br />
The present document is an introduction manual on how to use the crystal plasticity finite element method (CPFEM) for materials deformation simulation. CPFEM is based on a crystal plasticity constitutive model incorporated in the UMAT user subroutine of the commercial finite element software ABAQUS 6.9. The single crystal or polycrystal of face-centered cubic (FCC), body-centered cubic (BCC) and hexagonal closed (HCP) structures will respond to an applied stress by dislocation slip which is simulated using CPFEM. Orientations of grains will rotate during deformation. At the same time, the threshold stress of each slip systems will increase because of the self-hardening and latent hardening of the deformation modes. As such, the mechanical response (stress-strain curve) and the orientation of the crystals (texture) will be captured by the CPFEM. By comparing predicted results with experiments, one can get useful information about deformation mode activation, stress-strain data and crystal re-orientations, aspects that lead to a fundamentally understanding of the nature of metal deformation at the grain scale.<br />
<br />
The general workflow for running Crystal Plasticity simulations using ABAQUS is illustrated in the figure below:<br />
<br />
[[Image:CPFEM_workflow.PNG|center|895px|Workflow for running Crystal Plasticity simulations using ABAQUS ]]<br />
<br />
=== Crystal Plasticity FEM Models ===<br />
<br />
<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
==== Input files using CPFEM for an aluminum simulation====<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
==== Input files using CPFEM for a magnesium simulation====<br />
<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
==== Running CPFEM with a One Element Geometry====<br />
<br />
=====Step 1=====<br />
Have access to ABAQUS finite element software. The crystal plasticity files were composed for ABAQUS and will not work with alternative FEA codes.<br />
<br />
=====Step 2=====<br />
Create a new directory in a location in which you have permission to do so. Then download copies of all the input files and store them within the newly created directory.<br />
<br />
=====Step 3=====<br />
Open the file called: "umat_xtal.f", and locate the following lines: <pre> data filePath<br />
& /'/cavs/cmd/data1/users/qma/abaqus_xtalplas/oneelement/'/</pre><br />
<br />
The test located between the single quotes needs to be replaced with the path to the new directory.<br />
<br />
=====Step 4=====<br />
Open ABAQUS CAE and load the one element model called "oneelement.cae". Then set/verify the boundary conditions and generate a new input file. Alternatively there is a default input file: "oneelement.inp" that can be used.<br />
<br />
====Output files====<br />
<br />
<br />
Output files of CPFEM include the texture.txto, test.xtal.trss, test.xtal.strs, test.xtal.strn, test.xtal.efss and test.agg.efss. some output files will change according to the model development. The texture.txto contains the deformed texture at various strain levels. One can use this file to plot any pole figures and calculate orientation distribution functions (ODFs) using the texture software MTEX (a MATLAB tool box), or [[ICME Pole Figure Plot Function | this]] custom MATLAB function. The output file test.agg.effss includes the effective stress-strain data. At present, one can use the ABAQUS CAE to output any stress- strain data as shown in the Manual.<br />
<br />
====Users Manual====<br />
[[Media:Introduction to CPFEM manual-1.pdf | CPFEM Manual]]<br />
<br />
====CPFEM Simulation Aluminum Results====<br />
<br />
[[Media:CPFEM Simulation of Aluminum V2.pdf | CPFEM Simulation Aluminum Results]]<br />
<br />
====Example of polycrystal tension of an aluminum simulation====<br />
<br />
[[Image:tension 75%.jpg|center|700px]]<br />
<br />
----<br />
[[Multiscale_Simulations| back to the Multiscale Codes home page]]<br />
<br />
[[Category: Mesoscale]]<br />
[[Category: CPFEM]]<br />
[[Category: Tutorial]]<br />
[[Category: ABAQUS]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:12:14Z<p>Burcham: /* Abaqus CPFEM */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
<br />
===Abaqus CPFEM===<br />
A crystal plasticity model in the ABAQUS subroutine UMAT.<br />
<br />
==== Input files using CPFEM for an aluminum simulation====<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded from the [[cpfem decks]] repository (CAVS users only) , or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:fcc.sx| fcc.sx]]- single crystal parameters<br />
* [[Media:test.xtali | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
<br />
==== Input files using CPFEM for a magnesium simulation====<br />
The ABAQUS input decks and a step-by-step Tutorial on how to use them to run CPFEM simulations can be downloaded (CAVS users only) [[ABAQUS tutorials|here]], or can be viewed online by clicking on the name of each of the files below.<br />
<br />
* [[Media:umat_xtal.f | umat_xtal.f]]- constitutive model - polycrystal average model<br />
* [[texture.txti]] - initial orientation distribution<br />
* [[Media:hcp.sx| hcp.sx]]- single crystal parameters<br />
* [[Media:test.xtali_Mg | test.xtali]]- control for the time step and deformation<br />
* [[Media:params_xtal.inc | params_xtal.inc]] - number of slip systems<br />
* [[numbers.inc]] - numerical constants<br />
* [[vert_hcp_121.01]]- vertices parameters in Mg<br />
* [[vert_hcp_121.03]] - vertices parameters in Mg<br />
* [[vert_hcp_121.05]] - vertices parameters in Mg<br />
<br />
==MATLAB==<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
<br />
==Polymers==<br />
=== [[Thermoplastic Modeling|Thermoplastics]] ===<br />
The Mississippi State University Internal State Variable (ISV) model for thermoplastics (TPISV) version 1.0 is being released along with its model calibration tool (TPfit). The model equations and material model fits are decribed in Bouvard et al. [2010]<ref>J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variables Model for amorphous glassy polymers”, Acta Mechanica, 213(1), 71-96., 2010.[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA_2010.pdf ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA]</ref>. This polymer based ISV model is able to capture the history effects of a thermoplastic polymer tested under different stress states and strain rates. The modeling approach follows current methodologies used for metals <ref>Bamman, D.J., Chiesa, M.L., Johnson, G.C. : Modeling large deformation and failure in manufacturing processes. In: Tatsumi, T.,Wanatabe, E.,Kambe, T. (eds.) Theoretical and Applied Mechanics, pp. 359–376. Elsevier Science,USA(1996)</ref> based on a thermodynamic approach with internal state variables. Thus, the material departs from spring-dashpot based models generally used to predict the mechanical behavior of polymers. To select the internal state variables, we have used a hierarchical multiscale approach for bridging mechanisms from the molecular scale (see * [[MD_PE_deformation | Atomistic Deformation of Amorphous Polyethylene]]) to the continuum scale. The continuum constitutive model applied a formalism using a three-dimensional large deformation kinematics and thermodynamics framework. <br />
<br />
The 3D constitutive equations of the model were implemented in ABAQUS Explicit using a VUMAT subroutine. These equations were then simplified to the one-dimensional case in order to fit the model parameters using MATLAB software. <br />
<br />
To learn how to use the parameters fitting routine, you can refer to the documentation ([https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/MSU.CAVS.CMD.2010-R0008-TPgui-v1.1.doc?view=co TPgui report:MSU.CAVS.CMD.2010-R0008]; [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/TPgui/trunk/doc/TPgui-Tutorial.pptx?view=co TPGui tutorial]).<br />
<br />
A stand-alone TP tool is available from the [[CodeRepository:TP|online code repository]]. Please refer to the documentation ([https://icme.hpc.msstate.edu/cmddocs/TP/TPgui.html online help and tutorial]) to learn how to use this tool.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:07:26Z<p>Burcham: /* Tutorials */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
<br />
===Abaqus CPFEM===<br />
* [[Code: ABAQUS CPFEM]]<br />
<br />
==MATLAB==<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
<br />
==Polymers==<br />
An temperature dependent elasoviscoelastic-viscoplastic internal state variable (ISV) model is available from Mississippi State University. The formulation follows current internal state variable methodologies used for metals and departs from the spring-dashpot representation generally used to characterize the mechanical behavior of polymers like those used by <ref>Ames et al. in Int J Plast, 25, 1495–1539 (2009)</ref> and <ref>Anand and Gurtin in Int J Solids Struct, 40, 1465–1487 (2003)</ref>, <ref>Anand and Ames in Int J Plast, 22, 1123–1170 (2006)</ref>, <ref>Anand et al. in Int J Plast, 25, 1474–1494 (2009)</ref>. The selection of internal state variables was guided by a hierarchical multiscale modeling approach that bridged deformation mechanisms from the molecular dynamics scale (coarse grain model) to the continuum level. The model equations were developed within a large deformation kinematics and thermodynamics framework where the hardening behavior at large strains was captured using a kinematic-type hardening variable with two possible evolution laws: a current method based on hyperelasticity theory and an alternate method whereby kinematic hardening depends on chain stretching and material plastic flow. The three-dimensional equations were then reduced to the one-dimensional case to quantify the material parameters from monotonic compression test data at different applied strain rates. To illustrate the generalized nature of the constitutive model, material parameters were determined for four different amorphous polymers: polycarbonate, poly(methylmethacrylate), polystyrene, and poly(2,6-dimethyl-1,4-phenylene oxide). This model captures the complex character of the stress–strain behavior of these amorphous polymers for a range of strain rates.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T16:03:28Z<p>Burcham: /* MATLAB */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
=== TPISV ===<br />
<br />
==MATLAB==<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
==Metals==<br />
The Mississippi State University Internal State Variable (ISV) plasticity-damage model ([[Code: DMG|DMG]]) <br />
production version 1.0 is being released along with its model calibration tool (DMGfit). The <br />
model equations and material model fits are explained in [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/DMG/trunk/doc/MSU.CAVS.CMD.2009-R0010.pdf?view=co CAVS Technical Report: MSU.CAVS.CMD.2009-R0010.pdf]. This model is based upon Bammann, DJ, Chiesa, ML, Horstemeyer, MF, Weingarten, LI, "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. Wierzbicki and Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993 and Horstemeyer, MF, Lathrop, J, Gokhale, AM, and Dighe, M, "Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy," Theoretical and Applied Mech., Vol. 33, pp. 31-47, 2000. This model will predict the plasticity and failure in a metal alloy. It can be initialized to have different heterogeneous microstructures within the finite element mesh.<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T15:56:19Z<p>Burcham: /* Metals */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
===DMG v1.0===<br />
[[Code: DMG|MSU DMG v1.0]] is an example of a plasticity-damage internal state variable model<ref>Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993</ref> <ref>Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp. 31-47, 2000</ref>, which admits different grain sizes, particles sizes, particle volume fractions, pore sizes, and pore volume fractions within each continuum element. Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures can be garnered from the [[Particle Characterization with ImageJ|Image Analysis]] tools, which require only a picture with a measured scale bar for the picture. Once the material model is calibrated and validated at the macroscale, it can then be used for the structural scale simulations.<br />
<br />
A video tutorial for calibrating DMG is found [https://www.youtube.com/watch?v=6VMMCSZVyXo| here].<br />
<br />
An in depth written tutorial of DMGfit can be found [[DMGfit 55p v1p1|here]].<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:<br />
<br />
* one element compression for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Compression/ here]<br />
* one element compression for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Compression/ here] <br />
* one element tension for aluminum A356 (ABAQUS-Implicit) [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Tension/ here]<br />
* one element tension for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Tension/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Implicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Implicit_Shear/ here]<br />
* one element simple shear for aluminum A356 (ABAQUS-Explicit)[https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/single_element_Linux/A356_Explicit_Shear/ here]<br />
<br />
[[Media:OneElement-compression-A356-Abaqus-explicit.tar|One element explicit compression A356 input decks]]<br />
Model Validation simulations include the following:<br />
notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)<br />
<br />
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') [https://icme.hpc.msstate.edu/viewvc/CMD%20Codes%20Repository/inputDecks/abaqus_fem_decks/ here], or can be viewed online by clicking 'view' for each of the files.<br />
<br />
<br />
<br />
==MATLAB==<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
** [[DOE_with_MATLAB_4 | Design of Experiments with MATLAB: Part 4]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the dislocation dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T15:53:05Z<p>Burcham: /* Metals */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
==MATLAB==<br />
<br />
Getting started in Matlab<br />
* [[MATLAB_Tutorials | MATLAB Tutorials]]<br />
** [[MATLAB_Basics | How to use MATLAB: The Basics of MATLAB]]<br />
** [[MATLAB_Basics_2 | How to use MATLAB: The Basics of MATLAB 2]]<br />
** [[MATLAB_Import_Data | How to Import Data from a Textfile]]<br />
** [[MATLAB_Export_Data | How to Write Data to a Textfile]]<br />
** [[Stress-Strain Plot | How to make a stress-strain plot using MATLAB]]<br />
** [[Journal_Quality_Plotting | How to make a journal quality plot using MATLAB]]<br />
** [[Errorbars_Plot | Example: How to make a journal quality plot with errorbars]]<br />
** [[Image_Processing_with_MATLAB_1 | How to do basic image processing with MATLAB]]<br />
** [[DOE_with_MATLAB_1 | Design of Experiments with MATLAB: Part 1]]<br />
** [[DOE_with_MATLAB_2 | Design of Experiments with MATLAB: Part 2]]<br />
** [[DOE_with_MATLAB_3 | Design of Experiments with MATLAB: Part 3]]<br />
** [[DOE_with_MATLAB_4 | Design of Experiments with MATLAB: Part 4]]<br />
<br />
===Virtual Composite Structure Generator (VCSG)===<br />
<br />
VCSG generates composite structure representative volume elements (RVEs) based on user input.<br />
<br />
==Phase Field Modeling==<br />
[[Phase Field Modeling]]<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T15:40:30Z<p>Burcham: /* Polymers */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
<br />
==Phase Field Modeling==<br />
<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref>Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
*[[A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T15:38:42Z<p>Burcham: /* Metals */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.]]<br />
<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | nanoscale]] and the [[MaterialModels:_Macroscale | macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | microscale]] behavior to [[MaterialModels:_Macroscale | macroscale]] results.<br />
<br />
=Tutorials=<br />
<br />
[[Phase Field Modeling]]<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
== Metals ==<br />
===Aluminum===<br />
*[[Yield surface prediction of Aluminum on rolling]]<br />
*[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] <br />
<br />
===Magnesium===<br />
*[[A channel die compression simulation on Mg AM30]]<br />
*[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]]<br />
*[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] <br />
<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref>Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
[[Polymers_Home|Polymers Home]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==References==<br />
<references/><br />
<br />
<br />
== Further Reading ==<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T15:10:03Z<p>Burcham: /* Concrete */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
<br />
[[File:2D_meso_biax.gif|thumb|200px| True stress–true strain curves under tension comparing the thermoplastic internal state variable model over a range of temperatures with experiments for acrylonitrile butadiene styrene (ABS).]]<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | Nanoscale]] and the [[MaterialModels:_Macroscale | Macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | Microscale]] behavior to [[MaterialModels:_Macroscale | Macroscale]] results.<br />
<br />
=Tutorials=<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
<br />
<br />
== Metals ==<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
=== Metals Overview ===<br />
* [[:Category:Aluminum|Aluminium Research]] <br />
* [[:Category:Magnesium|Magnesium Research]] <br />
* [[:Category:Steel|Steel Research]]<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref group="Phasefield">Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
=== References pertaining to metals ===<br />
<references group="Phasefield"/><br />
<br />
====Multilayer Thin Films====<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
[[Polymers_Home|Polymers Home]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the [[MaterialModels:_Macroscale | macroscale]], but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==Free software==<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
<br />
=== Preprocessing & Postprocessing Codes ===<br />
<br />
This section includes codes used for preprocessing and postprocessing atomistic results. This section can also include scripts used to generate initial structures for inclusion in molecular dynamics simulations. Additionally, this subsection will include examples of xyz coordinate files that can be used in conjunction with the LAMMPS read_data command to upload.<br />
<br />
* Initial Structure Generation<br />
<br />
* Data Analysis and Plotting<br />
<br />
* Visualization<br />
<br />
<br />
<br />
<br />
==References==<br />
<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T14:51:47Z<p>Burcham: /* Concrete */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | Nanoscale]] and the [[MaterialModels:_Macroscale | Macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | Microscale]] behavior to [[MaterialModels:_Macroscale | Macroscale]] results.<br />
<br />
=Tutorials=<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
<br />
<br />
== Metals ==<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
=== Metals Overview ===<br />
* [[:Category:Aluminum|Aluminium Research]] <br />
* [[:Category:Magnesium|Magnesium Research]] <br />
* [[:Category:Steel|Steel Research]]<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref group="Phasefield">Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
=== References pertaining to metals ===<br />
<references group="Phasefield"/><br />
<br />
====Multilayer Thin Films====<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
[[Polymers_Home|Polymers Home]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
===Concrete===<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the macroscale, but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==Free software==<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
<br />
=== Preprocessing & Postprocessing Codes ===<br />
<br />
This section includes codes used for preprocessing and postprocessing atomistic results. This section can also include scripts used to generate initial structures for inclusion in molecular dynamics simulations. Additionally, this subsection will include examples of xyz coordinate files that can be used in conjunction with the LAMMPS read_data command to upload.<br />
<br />
* Initial Structure Generation<br />
<br />
* Data Analysis and Plotting<br />
<br />
* Visualization<br />
<br />
<br />
<br />
<br />
==References==<br />
<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T14:51:25Z<p>Burcham: /* Geomaterials */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | Nanoscale]] and the [[MaterialModels:_Macroscale | Macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | Microscale]] behavior to [[MaterialModels:_Macroscale | Macroscale]] results.<br />
<br />
=Tutorials=<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
<br />
<br />
== Metals ==<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
=== Metals Overview ===<br />
* [[:Category:Aluminum|Aluminium Research]] <br />
* [[:Category:Magnesium|Magnesium Research]] <br />
* [[:Category:Steel|Steel Research]]<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref group="Phasefield">Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
=== References pertaining to metals ===<br />
<references group="Phasefield"/><br />
<br />
====Multilayer Thin Films====<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
[[Polymers_Home|Polymers Home]]<br />
<br />
== Biomaterials==<br />
<br />
==Geomaterials==<br />
=Concrete=<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the macroscale, but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==Free software==<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
<br />
=== Preprocessing & Postprocessing Codes ===<br />
<br />
This section includes codes used for preprocessing and postprocessing atomistic results. This section can also include scripts used to generate initial structures for inclusion in molecular dynamics simulations. Additionally, this subsection will include examples of xyz coordinate files that can be used in conjunction with the LAMMPS read_data command to upload.<br />
<br />
* Initial Structure Generation<br />
<br />
* Data Analysis and Plotting<br />
<br />
* Visualization<br />
<br />
<br />
<br />
<br />
==References==<br />
<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T14:50:31Z<p>Burcham: /* Overview */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | Nanoscale]] and the [[MaterialModels:_Macroscale | Macroscale]]. This length scale aids in linking [[MaterialModels:_Microscale | Microscale]] behavior to [[MaterialModels:_Macroscale | Macroscale]] results.<br />
<br />
=Tutorials=<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
<br />
<br />
== Metals ==<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
=== Metals Overview ===<br />
* [[:Category:Aluminum|Aluminium Research]] <br />
* [[:Category:Magnesium|Magnesium Research]] <br />
* [[:Category:Steel|Steel Research]]<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref group="Phasefield">Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
=== References pertaining to metals ===<br />
<references group="Phasefield"/><br />
<br />
====Multilayer Thin Films====<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
[[Polymers_Home|Polymers Home]]<br />
<br />
== Biomaterials==<br />
<br />
=Geomaterials=<br />
==Concrete==<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the macroscale, but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==Free software==<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
<br />
=== Preprocessing & Postprocessing Codes ===<br />
<br />
This section includes codes used for preprocessing and postprocessing atomistic results. This section can also include scripts used to generate initial structures for inclusion in molecular dynamics simulations. Additionally, this subsection will include examples of xyz coordinate files that can be used in conjunction with the LAMMPS read_data command to upload.<br />
<br />
* Initial Structure Generation<br />
<br />
* Data Analysis and Plotting<br />
<br />
* Visualization<br />
<br />
<br />
<br />
<br />
==References==<br />
<br />
[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
<br />
[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
<br />
[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
<br />
[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
<br />
[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
<br />
[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
<br />
[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
<br />
[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
<br />
<br />
<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burchamhttps://icme.hpc.msstate.edu/mediawiki/index.php/Category:MesoscaleCategory:Mesoscale2016-03-14T14:40:01Z<p>Burcham: /* Geomaterials */</p>
<hr />
<div>__NOTOC__<br />
{{Menu_Models}}<br />
<br />
=Overview=<br />
"Mesoscale" refers to an ''intermediate'' length scale that spans the range between the [[MaterialModels:_Nanoscale | Nanoscale]] and the [[MaterialModels:_Macroscale | Macroscale]].<br />
<br />
=Tutorials=<br />
<br />
=Material Models=<br />
<br />
=Mesoscale Research=<br />
<br />
<br />
<br />
== Metals ==<br />
<br />
The mesoscale, although used generically to mean many things that are "intermediate," means essentially crystal plasticity in the context of multiscale modeling of metals. Crystal plasticity essentially is a continuum theory, but has discrete quantities starting at the grain or crystal scale. Polycrystalline averaging starting from the grain scale could be compared to the polycrystalline internal state variable models that operate at the [[Macroscale|macroscale]]. It can reach down to the Dislocation Dynamics results to help determine the material constants for the work hardening rules. Two different crystal plasticity formulations are given here:<br />
<br />
# Polycrystal formulations for [[Fcc|FCC]], [[Bcc|BCC]], and [[Hcp|HCP]] crystals<br />
# Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities<br />
<br />
Experiments for calibration (homogeneously applied stress and strain states) and validation (heterogeneous stress and strain states) are used to determine the material constants and particular microstructures. The microstructures of interest include the texture (grain/crystal orientation, stress-strain behavior, hardening response, and twinning response if needed). Once the material model is calibrated and validated at the mesoscale, the results for the texture, yield surface, and hardening evolutions can be used in the macroscale internal state variable model and [[Structural Scale|structural scale]] simulations. <br />
<br />
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined: <br />
<br />
* CPfit 1.0<br />
* VPSCfit 1.0<br />
<br />
The following single element finite element input decks should be used to verify the material point simulator determinations: <br />
one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) <br />
one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard)<br />
one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard) <br />
<br />
See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]]<br />
<br />
<br />
=== Metals Overview ===<br />
* [[:Category:Aluminum|Aluminium Research]] <br />
* [[:Category:Magnesium|Magnesium Research]] <br />
* [[:Category:Steel|Steel Research]]<br />
<br />
===[[Phase Field Modeling]] of Microstructural Evolution===<br />
A broad spectrum of moving boundary problems can be successfully handled with the diffuse-interface or phase-ﬁeld<br />
models. Such models are constructed by assuming that the free energy of a non-uniform system F, depends on (among other<br />
variables) the phase-ﬁeld variable <math>\boldsymbol{\phi}</math>, and its gradient <math> {\bigtriangledown}{\phi}</math>. In the volume V:<br />
<br />
F = <math>\int\limits_{V}g \left ( {\phi}, {\bigtriangledown} {\phi} \right )dV</math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (1)<br />
<br />
Mathematically, the phase-ﬁeld formulation gives rise to two types of problems.<br />
The non-conserved phase-ﬁeld variables, such as those in solidiﬁcation and melting problems, are often assumed to<br />
evolve according to the ‘‘ﬁrst-order relaxation”, whereby the rate of change of the phase variable,<br />
<math>\dot{\phi}</math>, is proportional to the<br />
variational derivative of the free energy, mediated by the kinetic mobility B:<br />
<br />
<math>\dot{\phi}</math> = <math>-\boldsymbol B{\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi}</math><br />
<br />
Such a formulation leads to a 2nd order, diffusion-type partial differential equation (PDE) for <math>\boldsymbol{\phi}</math>. However, if the phase-<br />
ﬁeld variable is subject to a conservation law, e.g.<br />
<br />
<math>\frac{d}{dt}\int\limits_{V}{\phi} dV = 0 </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (2)<br />
<br />
then the rate <math>\dot{\phi}</math> is proportional to the divergence of the ﬂux, which in turn, is proportional to the gradient of a potential. This potential is equal to the variational derivative of the free energy:<br />
<br />
<math>\dot{\phi}</math>= <math> -{\bigtriangledown}.</math><math> \quad \left \lbrack -B {\bigtriangledown} \left ({\boldsymbol{\delta}F}/\boldsymbol{\delta}\boldsymbol{\phi} \right ) \right \rbrack </math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; (3)<br />
<br />
Examples include diffusion-controlled solid-state phase transformations, and interfaces between immiscible ﬂuids<br />
. Typically, the 4th order evolution PDE (3) is coupled to a 2nd order PDEs (stress, heat, etc.). For example, in solid<br />
state phase transformations, the lattice continuity across the interfaces between mismatched phases produces elastic strains<br />
, so that the 2nd order elasticity PDEs are coupled to the phase ﬁeld Eq. (3).<br />
The problems in this class have been addressed in the past, with the numerical tools tailored for speciﬁc problems. However, a general numerical method for solving the coupled equations, applicable to a variety of geometries and boundary conditions, has remained a challenging problem. The ﬁnite difference method (FDM) was used by Cahn and Kobayashi for<br />
one-dimensional modeling of the rapid coarsening and buckling in coherently self-stressed thin plates. Johnson used<br />
FDM to study the growth of the intermediate phase in a thin ﬁlm diffusion couple. Leo et al.used a pseudo-spectral<br />
method for the phase-ﬁeld model of coarsening in a two dimensional, elastically stressed, binary alloys. Fourier transform<br />
techniques, and related Fourier-spectral methods , have been used to investigate the microstructure evolution (mostly coarsening) resulting from solid-state phase transformations. The drawbacks of such methods are seen when<br />
the problem requires modeling of irregular domains, nonlinear and history-dependent problems. A versatile method is<br />
needed, applicable to irregular domains, a variety of boundary conditions, and various forms of geometric and material nonlinearities. The ﬁnite element method (FEM) and the related mesh-free method are such methods.<br />
<ref group="Phasefield">Mohsen Asle Zaeem, Sinisa Dj. Mesarovic, Finite element method for conserved phase fields: Stress-mediated diffusional phase transformation Original Research Article<br />
''Journal of Computational Physics'', Volume 229, Issue 24, 10 December 2010, Pages 9135-9149</ref><br />
<br />
=== References pertaining to metals ===<br />
<references group="Phasefield"/><br />
<br />
====Multilayer Thin Films====<br />
<br />
== Ceramics==<br />
<br />
== Polymers==<br />
<br />
[[Polymers_Home|Polymers Home]]<br />
<br />
== Biomaterials==<br />
<br />
=Geomaterials=<br />
==Concrete==<br />
Analysis of concrete at the mesoscale is beneficial as the size and distribution of constituents becomes evident. Concrete is a composite material made up of aggregates surrounded by a matrix. Large aggregates are easily visible at the macroscale, but small aggregates, unhydrated cement grains, and voids are first visible at the mesoscale.<br />
<br />
==Free software==<br />
<br />
Matlab tool box for texture MTEX<br />
<br />
*MTEX [http://code.google.com/p/mtex/]<br />
<br />
<br />
=== Preprocessing & Postprocessing Codes ===<br />
<br />
This section includes codes used for preprocessing and postprocessing atomistic results. This section can also include scripts used to generate initial structures for inclusion in molecular dynamics simulations. Additionally, this subsection will include examples of xyz coordinate files that can be used in conjunction with the LAMMPS read_data command to upload.<br />
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* Initial Structure Generation<br />
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* Data Analysis and Plotting<br />
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* Visualization<br />
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==References==<br />
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[1] [[Media:ref.txt.pdf|E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170.]].<br />
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[2] S. Groh, E.B. Marin, M.F. Horstemeyer, et al., Multiscale modeling of the plasticity in an aluminum single crystal, International Journal of Plasticity, 25(2009), 1456-1473.<br />
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[3] E.B. Marin, P.R. Dawson, On modeling the elasto-viscoplastic response of metals using polycrystal plasticity, Computer Methods in Applied Mechanics and Engineering, 165(1998), 1-21.<br />
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[4] E.B. Marin, P.R. Dawson, J.T. Jenkins, Aggregate size effect on the predicted plastic response of hexagonal close-packed polycrystals, Modelling Simulation Materials Science Engineering, 3(1995), 845-864. <br />
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[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.<br />
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[6] F. Roters, P. Eisenlohr, L. Hantcherli, et al., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia, 58(2010), 1152-1211.<br />
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[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.<br />
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[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.<br />
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<!--Categories--><br />
[[Category:Overview]]<br />
[[Category:Metals]]<br />
[[Category:Polymers]]<br />
[[Category:Multiscale Simulations]]</div>Burcham