Micromechanics and nonlocal effects in graded random structure matrix composites

We consider Functionally Graded Materials (FGMs) as a Linear thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal inclusions, when the concentration of the inclusions is a function of the coordinates and the meso-stress boundary condition are nonuniform. The micromechanical approach is based on the generalization of the "multiparticle effective field" method (MEFM), previously proposed for statistically homogeneous random structure composites by one of the present authors. The hypothesis of effective field homogeneity near the inclusions is used. The nonlocal dependences of the effective elastic moduli as well as of conditional averages of the strains in the components on the concentration of the inclusions are demonstrated. An explicit representation for the operator of effective properties in the form of a differential operator of second order acting on a sufficiently slowly varying ensemble average strain field is obtained.