Recurrent approach to effective material properties with application to anisotropic binarized random fields

Abstract

Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions, providing a recurrent series expansion of the effective permittivity to arbitrary order. Within this framework, we also demonstrate a progressive method to determine tight bounds that converge towards the exact solution. We illustrate the utility of these methods by using ensemble averaging to determine the micro-structural parameters of anisotropic level-cut Gaussian fields. We find that the depolarization factor of these structures is equivalent to that of an isolated ellipse with the same stretchingratio, and discuss the contribution of the fourth order term to the exact anisotropy.