Multiparticle effective field and related methods in micromechanics of random structure components

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 components are estimated for both the general case of nonhomogeneity of the thermoelastic inclusion properties and arbitrary choice of comparison medium. The micromechanical approach is based on Green's function techniques as well as on the generalization of the "multiparticle effective field" method (MEFM), previously proposed for the estimation of stress field averages in the components for the case of coinciding elastic moduli of the matrix and comparison medium. The author considers in detail the connection of methods proposed with numerous related methods and demonstrates that the MEFM includes, as particular cases, the well-known methods of mechanics of strongly heterogeneous media (such as the effective medium and the mean field methods and some others).