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Title: Computational Mechanics for Heterogeneous Materials

Abstract

The subject of this work is the development of models for the numerical simulation of matter, momentum, and energy balance in heterogeneous materials. These are materials that consist of multiple phases or species or that are structured on some (perhaps many) scale(s). By computational mechanics we mean to refer generally to the standard type of modeling that is done at the level of macroscopic balance laws (mass, momentum, energy). We will refer to the flow or flux of these quantities in a generalized sense as transport. At issue here are the forms of the governing equations in these complex materials which are potentially strongly inhomogeneous below some correlation length scale and are yet homogeneous on larger length scales. The question then becomes one of how to model this behavior and what are the proper multi-scale equations to capture the transport mechanisms across scales. To address this we look to the area of generalized stochastic process that underlie the transport processes in homogeneous materials. The archetypal example being the relationship between a random walk or Brownian motion stochastic processes and the associated Fokker-Planck or diffusion equation. Here we are interested in how this classical setting changes when inhomogeneities or correlations inmore » structure are introduced into the problem. Aspects of non-classical behavior need to be addressed, such as non-Fickian behavior of the mean-squared-displacement (MSD) and non-Gaussian behavior of the underlying probability distribution of jumps. We present an experimental technique and apparatus built to investigate some of these issues. We also discuss diffusive processes in inhomogeneous systems, and the role of the chemical potential in diffusion of hard spheres is considered. Also, the relevance to liquid metal solutions is considered. Finally we present an example of how inhomogeneities in material microstructure introduce fluctuations at the meso-scale for a thermal conduction problem. These fluctuations due to random microstructures also provide a means of characterizing the aleatory uncertainty in material properties at the mesoscale.« less

Authors:
 [1];  [1]; ;  [1];  [1];  [1];  [1];  [1];  [1];  [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1325910
Report Number(s):
SAND2013-10063
587677
DOE Contract Number:
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Lechman, Jeremy B., Baczewski, Andrew David, Stephen Bond, Erikson, William W., Lehoucq, Richard B., Mondy, Lisa Ann, Noble, David R., Pierce, Flint, Roberts, Christine, van Swol, Frank B., and Yarrington, Cole. Computational Mechanics for Heterogeneous Materials. United States: N. p., 2013. Web. doi:10.2172/1325910.
Lechman, Jeremy B., Baczewski, Andrew David, Stephen Bond, Erikson, William W., Lehoucq, Richard B., Mondy, Lisa Ann, Noble, David R., Pierce, Flint, Roberts, Christine, van Swol, Frank B., & Yarrington, Cole. Computational Mechanics for Heterogeneous Materials. United States. doi:10.2172/1325910.
Lechman, Jeremy B., Baczewski, Andrew David, Stephen Bond, Erikson, William W., Lehoucq, Richard B., Mondy, Lisa Ann, Noble, David R., Pierce, Flint, Roberts, Christine, van Swol, Frank B., and Yarrington, Cole. Fri . "Computational Mechanics for Heterogeneous Materials". United States. doi:10.2172/1325910. https://www.osti.gov/servlets/purl/1325910.
@article{osti_1325910,
title = {Computational Mechanics for Heterogeneous Materials},
author = {Lechman, Jeremy B. and Baczewski, Andrew David and Stephen Bond and Erikson, William W. and Lehoucq, Richard B. and Mondy, Lisa Ann and Noble, David R. and Pierce, Flint and Roberts, Christine and van Swol, Frank B. and Yarrington, Cole},
abstractNote = {The subject of this work is the development of models for the numerical simulation of matter, momentum, and energy balance in heterogeneous materials. These are materials that consist of multiple phases or species or that are structured on some (perhaps many) scale(s). By computational mechanics we mean to refer generally to the standard type of modeling that is done at the level of macroscopic balance laws (mass, momentum, energy). We will refer to the flow or flux of these quantities in a generalized sense as transport. At issue here are the forms of the governing equations in these complex materials which are potentially strongly inhomogeneous below some correlation length scale and are yet homogeneous on larger length scales. The question then becomes one of how to model this behavior and what are the proper multi-scale equations to capture the transport mechanisms across scales. To address this we look to the area of generalized stochastic process that underlie the transport processes in homogeneous materials. The archetypal example being the relationship between a random walk or Brownian motion stochastic processes and the associated Fokker-Planck or diffusion equation. Here we are interested in how this classical setting changes when inhomogeneities or correlations in structure are introduced into the problem. Aspects of non-classical behavior need to be addressed, such as non-Fickian behavior of the mean-squared-displacement (MSD) and non-Gaussian behavior of the underlying probability distribution of jumps. We present an experimental technique and apparatus built to investigate some of these issues. We also discuss diffusive processes in inhomogeneous systems, and the role of the chemical potential in diffusion of hard spheres is considered. Also, the relevance to liquid metal solutions is considered. Finally we present an example of how inhomogeneities in material microstructure introduce fluctuations at the meso-scale for a thermal conduction problem. These fluctuations due to random microstructures also provide a means of characterizing the aleatory uncertainty in material properties at the mesoscale.},
doi = {10.2172/1325910},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Nov 01 00:00:00 EDT 2013},
month = {Fri Nov 01 00:00:00 EDT 2013}
}

Technical Report:

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