Details
| Original language | English |
|---|---|
| Pages (from-to) | 69-88 |
| Number of pages | 20 |
| Journal | Computational materials science |
| Volume | 15 |
| Issue number | 1 |
| Publication status | Published - 24 May 1999 |
Abstract
In this paper the pressure dependence of macroscopic of "homogenized" diffusive properties of materials containing heterogeneities is investigated. The model involves a pressure dependent regularization of the spatially variable material, by a relation between averages over statistically representative samples subjected to various pressure loadings. The pressure dependence of the local diffusive properties enters through an Arhennius type model. In the regularization process the boundary value problems are posed over the statistically representative samples of material. By definition, such samples contain a large number of heterogeneities, and thus the associated numerical computations require extremely high nodal mesh densities to capture the irregular oscillatory internal fields. In order to simplify the problem, the pressure fields are approximated, above and below in an energetic sense, via classical extremal methods. With these approximations, the pointwise diffusivity coefficients are constructed as a function of pressure. Further approximations are made of the internal geometry by employing a technique of Huet et al. [13]. This allows the use of a Cartesian geometry that can be easily handled with a finite difference scheme. With these approximations, numerical simulations are performed to investigate the regularized macroscopic diffusive properties as a function of macroscopic applied pressure.
Keywords
- Coupled fields, Diffusion, Heterogeneous materials, Regularization
ASJC Scopus subject areas
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In: Computational materials science, Vol. 15, No. 1, 24.05.1999, p. 69-88.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A technique to describe the macroscopic pressure dependence of diffusive properties of solid materials containing heterogeneities
AU - Zohdi, T. I.
AU - Hutter, K.
AU - Wriggers, Peter
PY - 1999/5/24
Y1 - 1999/5/24
N2 - In this paper the pressure dependence of macroscopic of "homogenized" diffusive properties of materials containing heterogeneities is investigated. The model involves a pressure dependent regularization of the spatially variable material, by a relation between averages over statistically representative samples subjected to various pressure loadings. The pressure dependence of the local diffusive properties enters through an Arhennius type model. In the regularization process the boundary value problems are posed over the statistically representative samples of material. By definition, such samples contain a large number of heterogeneities, and thus the associated numerical computations require extremely high nodal mesh densities to capture the irregular oscillatory internal fields. In order to simplify the problem, the pressure fields are approximated, above and below in an energetic sense, via classical extremal methods. With these approximations, the pointwise diffusivity coefficients are constructed as a function of pressure. Further approximations are made of the internal geometry by employing a technique of Huet et al. [13]. This allows the use of a Cartesian geometry that can be easily handled with a finite difference scheme. With these approximations, numerical simulations are performed to investigate the regularized macroscopic diffusive properties as a function of macroscopic applied pressure.
AB - In this paper the pressure dependence of macroscopic of "homogenized" diffusive properties of materials containing heterogeneities is investigated. The model involves a pressure dependent regularization of the spatially variable material, by a relation between averages over statistically representative samples subjected to various pressure loadings. The pressure dependence of the local diffusive properties enters through an Arhennius type model. In the regularization process the boundary value problems are posed over the statistically representative samples of material. By definition, such samples contain a large number of heterogeneities, and thus the associated numerical computations require extremely high nodal mesh densities to capture the irregular oscillatory internal fields. In order to simplify the problem, the pressure fields are approximated, above and below in an energetic sense, via classical extremal methods. With these approximations, the pointwise diffusivity coefficients are constructed as a function of pressure. Further approximations are made of the internal geometry by employing a technique of Huet et al. [13]. This allows the use of a Cartesian geometry that can be easily handled with a finite difference scheme. With these approximations, numerical simulations are performed to investigate the regularized macroscopic diffusive properties as a function of macroscopic applied pressure.
KW - Coupled fields
KW - Diffusion
KW - Heterogeneous materials
KW - Regularization
UR - http://www.scopus.com/inward/record.url?scp=0345770637&partnerID=8YFLogxK
U2 - 10.1016/S0927-0256(99)00010-5
DO - 10.1016/S0927-0256(99)00010-5
M3 - Article
AN - SCOPUS:0345770637
VL - 15
SP - 69
EP - 88
JO - Computational materials science
JF - Computational materials science
SN - 0927-0256
IS - 1
ER -