Generalization of the multiparticle effective field method to random structure matrix composites

Abstract

In this paper linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance, thermal expansion, stored energy) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the generalization of the ``multiparticle effective field'' method (MEFM, see [7] for references), previously proposed for the estimation of stress field averages in the phases. The refined version of the MEFM takes into account both the variation of the effective fields acting on each pair of fibers and inhomogeneity of statistical average of stresses inside the inclusions. One considers in detail the connection of the method proposed with numerous related methods. The explicit representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to the homogeneous loading at infinity. Just with some additional assumptions (such as an effective field hypothesis) the involved tensors can be expressed through the Green's function, Eshelby tensor and external Eshelby tensor. The dependence of effective properties and stress concentrator factors on the radial distribution function of the inclusion locations is analyzed.