A technique to describe the macroscopic pressure dependence of diffusive properties of solid materials containing heterogeneities

authored by: T. I. Zohdi, K. Hutter, Peter Wriggers
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.
Organisation(s): Institute of Mechanics and Computational Mechanics
External Organisation(s): Technische Universität Darmstadt
Type: Article
Journal: Computational materials science
Volume: 15
Pages: 69-88
No. of pages: 20
ISSN: 0927-0256
Publication date: 24.05.1999
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computer Science(all), Chemistry(all), Materials Science(all), Mechanics of Materials, Physics and Astronomy(all), Computational Mathematics
Electronic version(s): https://doi.org/10.1016/S0927-0256(99)00010-5 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{fc7c758eab004563b874f85a734271b9,
title = "A technique to describe the macroscopic pressure dependence of diffusive properties of solid materials containing heterogeneities",
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",
author = "Zohdi, {T. I.} and K. Hutter and Peter Wriggers",
year = "1999",
month = may,
day = "24",
doi = "10.1016/S0927-0256(99)00010-5",
language = "English",
volume = "15",
pages = "69--88",
journal = "Computational materials science",
issn = "0927-0256",
publisher = "Elsevier",
number = "1",
}