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MSU DMG v1.0 is an example of a plasticity-damage internal state variable model , 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 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.
A video tutorial for calibrating DMG is found here.
An in depth written tutorial of DMGfit can be found here.
The following single element finite element input decks should be used to verify the material point simulator (DMGfit) determinations:
- one element compression for aluminum A356 (ABAQUS-Implicit)here
- one element compression for aluminum A356 (ABAQUS-Explicit)here
- one element tension for aluminum A356 (ABAQUS-Implicit) here
- one element tension for aluminum A356 (ABAQUS-Explicit)here
- one element simple shear for aluminum A356 (ABAQUS-Implicit)here
- one element simple shear for aluminum A356 (ABAQUS-Explicit)here
One element explicit compression A356 input decks Model Validation simulations include the following: notch tensile specimen (1/8 space mesh) for aluminum A356 (ABAQUS-Implicit)
The ABAQUS input decks and instruction on how to one element simulations can be downloaded ('Download GNU tarball') here, or can be viewed online by clicking 'view' for each of the files.
Getting started in Matlab
- MATLAB Tutorials
- How to use MATLAB: The Basics of MATLAB
- How to use MATLAB: The Basics of MATLAB 2
- How to Import Data from a Textfile
- How to Write Data to a Textfile
- How to make a stress-strain plot using MATLAB
- How to make a journal quality plot using MATLAB
- Example: How to make a journal quality plot with errorbars
- How to do basic image processing with MATLAB
- Design of Experiments with MATLAB: Part 1
- Design of Experiments with MATLAB: Part 2
- Design of Experiments with MATLAB: Part 3
Virtual Composite Structure Generator (VCSG)
VCSG generates composite structure representative volume elements (RVEs) based on user input.
Phase Field Modeling
The Mississippi State University Internal State Variable (ISV) plasticity-damage model (DMG) production version 1.0 is being released along with its model calibration tool (DMGfit). The model equations and material model fits are explained in 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.
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  and , , . 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.
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. 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:
- Polycrystal formulations for FCC, BCC, and HCP crystals
- Visco Plasticity Self Consistent (VPSC) model: polycrystalline averaged quantities
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 simulations.
Model Calibration for both the CP 1.0 and VPSC 1.0 models have fitting algorithms in which the material constants can be determined:
- CPfit 1.0
- VPSCfit 1.0
The following single element finite element input decks should be used to verify the material point simulator determinations: one element compression for 500 crystals aluminum polycrystal(ABAQUS-Standard) one element tension for 500 crystals aluminum polycrystal(ABAQUS-Standard) one element simple shear for 500 crystals aluminum polycrystal (ABAQUS-Standard)
See also: ABAQUS CPFEM
- Yield surface prediction of Aluminum on rolling
- Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum
- One element deformation of Aluminum
- A channel die compression simulation on Mg AM30
- Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy
- One element deformation of Magnesium
Phase Field Modeling of Microstructural Evolution
- A mesomechanics parametric finite element study of damage growth and coalescence in polymers using an Elastoviscoelastic-Viscoplastic internal state variable model
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.
- ↑ 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
- ↑ 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
- ↑ Ames et al. in Int J Plast, 25, 1495–1539 (2009)
- ↑ Anand and Gurtin in Int J Solids Struct, 40, 1465–1487 (2003)
- ↑ Anand and Ames in Int J Plast, 22, 1123–1170 (2006)
- ↑ Anand et al. in Int J Plast, 25, 1474–1494 (2009)
 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.
 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.
 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.
 F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.
 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.
 D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.
 D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.
This category has the following 3 subcategories, out of 3 total.
Pages in category "Mesoscale"
The following 44 pages are in this category, out of 44 total.
Media in category "Mesoscale"
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- Shi input data.PNG