Abstract :
Recent progress that we have made on the problem of determining the effective 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 electrical
conductivity of composites, time scales associated with diffusion and reaction among traps, and
fluid permeability of porous media. We also remark on the importance of microstructure fluctuations
in influencing the failure characteristics of composites. The preponderance of work thus far has
focused on heterogeneous media that are statistically homogeneous. We propose a model for
statistically inhomogeneous two-phase random media (including functionally graded materials)
consisting of 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 statistically homogeneous media, the microstructure functions depend upon
the absolute positions of their arguments. Finally, we describe a novel procedure to reconstruct
heterogeneous media from limited knowledge about the microstructure and discuss applications of
this technique. © 1998 Elsevier Science Ltd. All rights reserved
