Microstructure functions for a model of statistically inhomogeneous random media

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. © 1998 The American Physical Society.