# Category:Mesoscale

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== Metals == | == Metals == | ||

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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: | 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: | ||

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See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]] | See also: [[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|ABAQUS CPFEM]] | ||

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+ | ===Aluminum=== | ||

+ | *[[Yield surface prediction of Aluminum on rolling]] | ||

+ | *[[Visco-Plastic Self-Consistent (VPSC) Deformation Simulation of Polycrystalline FCC Aluminum]] | ||

+ | *[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Aluminum]] | ||

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+ | ===Magnesium=== | ||

+ | *[[A channel die compression simulation on Mg AM30]] | ||

+ | *[[Twinning and double twinning upon compression of prismatic textures in an AM30 magnesium alloy]] | ||

+ | *[[Code:_ABAQUS_CPFEM#Crystal_Plasticity_Finite_Element_Method|One element deformation of Magnesium]] | ||

## Revision as of 09:53, 14 March 2016

Metals • Ceramics • Polymers • Biomaterials • Geomaterials • References

# 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

## 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
- Design of Experiments with MATLAB: Part 4

### Virtual Composite Structure Generator (VCSG)

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

## Phase Field Modeling

# Material Models

# 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

### 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

## 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"

This category contains only the following file.