Abstract

We propose a model for statistically inhomogeneous two-phase random media, including functionally graded materials, consisting of inhomogeneous fully penetrable (Poisson distributed) spheres. This model can be constructed for any specified variation of volume fraction and 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. However, as with homogeneous random media, this microstructural information will be useful in obtaining rigorous estimates of the effective properties of such systems. Typeset using REVT E X I. INTRODUCTION Much progress has been made in recent years in characterizing the microstructure of statistically homogeneous two-phase random media via a variety of n-point correlation functions [1--3]. For ergodic ensembles, the n-point correlation func...

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