MORPHOLOGY AND EFFECTIVE PROPERTIES OF DISORDERED HETEROGENEOUS MEDIA

Recent progress that we have made on the problem of determining the ef fective properties of random heterogeneous media from knowledge of the morphology is reviewed and extended. A variety of different effective properties are considered, including the elastic moduli and electrica l conductivity of composites, time scales associated with diffusion an d reaction among traps, and fluid permeability of porous media. We als o remark on the importance of microstructure fluctuations in influenci ng the failure characteristics of composites. The preponderance of wor k thus far has focused on heterogeneous media that are statistically h omogeneous. We propose a model for statistically inhomogeneous two-pha se random media (including functionally graded materials) consisting O f inhomogeneous fully penetrable spheres that permits one to represent and evaluate certain n-point correlation functions that statistically characterize the microstructure for this model. Unlike the case of st atistically homogeneous media, the microstructure functions depend upo n the absolute positions of their arguments. Finally, we describe a no vel procedure to reconstruct heterogeneous media from limited knowledg e about the microstructure and discuss applications of this technique. (C) 1998 Elsevier Science Ltd. All rights reserved.