Category:Mesoscale

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=== TPISV ===
 
=== TPISV ===
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===Abaqus CPFEM===
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* [[Code: ABAQUS CPFEM]]
  
 
==MATLAB==
 
==MATLAB==

Revision as of 11:07, 14 March 2016

MetalsCeramicsPolymersBiomaterialsGeomaterialsReferences

Overview

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Biaxial loading of a 9x9 mm Polycarbonate plate with 2 defects.

"Mesoscale" refers to an intermediate length scale that spans the range between the nanoscale and the macroscale. This length scale aids in linking microscale behavior to macroscale results.

Tutorials

DMG v1.0

MSU DMG v1.0 is an example of a plasticity-damage internal state variable model[1] [2], 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.


TPISV

Abaqus CPFEM

MATLAB

Getting started in Matlab

Virtual Composite Structure Generator (VCSG)

VCSG generates composite structure representative volume elements (RVEs) based on user input.

Phase Field Modeling

Phase Field Modeling

Material Models

Metals

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.


Polymers

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 [3] and [4], [5], [6]. 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.

Mesoscale Research

Metals

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:

  1. Polycrystal formulations for FCC, BCC, and HCP crystals
  2. 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

Aluminum

Magnesium


Phase Field Modeling of Microstructural Evolution

Ceramics

Polymers

Biomaterials

Geomaterials

Concrete

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.

References

  1. 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
  2. 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
  3. Ames et al. in Int J Plast, 25, 1495–1539 (2009)
  4. Anand and Gurtin in Int J Solids Struct, 40, 1465–1487 (2003)
  5. Anand and Ames in Int J Plast, 22, 1123–1170 (2006)
  6. Anand et al. in Int J Plast, 25, 1474–1494 (2009)


Further Reading

[1] E.B. Marin, On the formulation of a crystal plasticity model, Sandia National Laboratories, CA, 2006, SAND2006-4170..

[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.

[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.

[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.

[5] F. Roters, Application of crystal plasticity FEM from single crystal to bulk polycrystal, Computational Materials Science, 32(2005), 509-517.

[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.

[7] D. Peirce, R.J. Asaro, A. Needleman, Analysis of nonuniform and localized deformation in FCC single crystals, Acta Metallurgica, 30(1982), 1087-1119.

[8] D. Peirce, R.J. Asaro, A. Needleman, Material rate dependence and localized deformation in crystalline solids, Acta Metallurgica, 31(1983), 1951-1976.

Subcategories

This category has the following 3 subcategories, out of 3 total.

Pages in category "Mesoscale"

The following 42 pages are in this category, out of 42 total.

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Media in category "Mesoscale"

This category contains only the following file.

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