# Category:Mesoscale

Metals • Ceramics • Polymers • Biomaterials • Geomaterials • References

## Contents |

# Overview

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"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

### Plasticity-Damage (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

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.

- One element compression for aluminum A356 (ABAQUS-Explicit) -here

### Abaqus CPFEM

A crystal plasticity model in the ABAQUS subroutine UMAT.

**Input files using CPFEM for an aluminum simulation**

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.

- umat_xtal.f- constitutive model - polycrystal average model
- texture.txti - initial orientation distribution
- fcc.sx- single crystal parameters
- test.xtali- control for the time step and deformation
- params_xtal.inc - number of slip systems
- numbers.inc - numerical constants

**Input files using CPFEM for a magnesium simulation**

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) here, or can be viewed online by clicking on the name of each of the files below.

- umat_xtal.f- constitutive model - polycrystal average model
- texture.txti - initial orientation distribution
- hcp.sx- single crystal parameters
- test.xtali- control for the time step and deformation
- params_xtal.inc - number of slip systems
- numbers.inc - numerical constants
- vert_hcp_121.01- vertices parameters in Mg
- vert_hcp_121.03 - vertices parameters in Mg
- vert_hcp_121.05 - vertices parameters in Mg

### MATLAB

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

### Dream 3D

3D reconstruction tool Dream.3D website

### Los Alamos Polycrystal Plasticity (LAPP)

Texture code that quantifies pole figures

by Fred Cox: LANL

### Microstructure Builder

Simulated 3D polycrystalline material creator

### Virtual Composite Structure Generator (VCSG)

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

### Visco-Plastic Self-Consistent (VPSC)

Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum

## Phase Field Modeling

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. Phase Field Modeling

## Material Texture

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).

# 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 the 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.

## Polymers

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]^{[3]}. 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 ^{[4]} 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 * 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.

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.

To learn how to use the parameters fitting routine, you can refer to the documentation (TPGui User Manual; TPGui Tutorial).

A stand-alone TP tool is available from the online code repository. Please refer to the documentation (online help and tutorial) to learn how to use this tool.

# 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:

- 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

### Aluminum

- Yield surface prediction of Aluminum on rolling
- Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum
- One element deformation of Aluminum

### Magnesium

- 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

## Ceramics

## Polymers

### Acrylonitrile Butadeine Styrene (ABS)

### Polycarbonate (PC)

## Biomaterials

## Geomaterials

### Concrete

## References

- ↑ 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
- ↑ 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.ISV_MODEL_POLYMER_PAPER_ACTAMECHANICA
- ↑ 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)

## Further Reading

[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 44 pages are in this category, out of 44 total.

## Media in category "Mesoscale"

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