Inhomogeneity of the first and second statistical moments of stresses inside the heterogeneities of random structure matrix composites

In this paper linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of heterogeneities. 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 for references Buryachenko, Appl. Mech. Rev. (2001), 54, 1–47), previously proposed for the estimation of stress field averages in the phases. The method exploits as a background the new general integral equation proposed by the author before and makes it possible to abandon the use of the central concept of classical micromechanics such as effective field hypothesis as well as their satellite hypothesis of “ellipsoidal symmetry”. The implicit recursion 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 inhomogeneous effective fields evaluated from subsequent self-consistent estimations. One also estimates the inhomogeneous statistical moments of local stress fields which are extremely useful for understanding the evolution of nonlinear phenomena such as plasticity, creep, and damage. Just at some additional assumptions (such as an effective field hypothesis) the involved tensors can be expressed through the Green function, Eshelby tensor and external Eshelby tensor. These estimated inhomogeneities of effective fields lead to the detection of fundamentally new effects for the local stresses inside the heterogeneities.