Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. I. Perturbation expansions for the effective permittivity of cell materials

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Abstract
A perturbation formulation is developed for the effective permittivity of random heterogeneous materials that are statistically homogeneous but not necessarily statistically isotropic. The formal perturbation solution is expressed explicitly by means of the many‐point correlation functions of the permittivity field. For a broad class of random multiphase materials called cell materials, the second‐ and third‐order perturbation effects are determined as functions of the depolarizing factor tensors of cells. In the special case where the medium is statistically isotropic, the formulas giving the effective permittivity to third order are shown to be in substantial accord with the results obtained by previous investigators.