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

In this paper the pressure dependence of macroscopic of "homogenized" diffu sive properties of materials containing heterogeneities is investigated. Th e model involves a pressure dependent regularization of the spatially varia ble material, by a relation between averages over statistically representat ive 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 th e statistically representative samples of material. By definition, such sam ples contain a large number of heterogeneities, and thus the associated num erical 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 sen se, via classical extremal methods. With these approximations, the pointwis e diffusivity coefficients are constructed as a function of pressure. Furth er approximations are made of the internal geometry by employing a techniqu e 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 approximatio ns, numerical simulations are performed to investigate the regularized macr oscopic diffusive properties as a function of macroscopic applied pressure. (C) 1999 Elsevier Science B.V. All rights reserved.