Bounds on the effective properties of some multiphase matrix mixtures of coated-sphere geometry

Some matrix multiphase mixtures of Hashin's coated-sphere assemblage geometry with homogeneous spherical inclusions, coated by spherical shells made from an isotropic matrix-phase are considered. The inclusions are randomly assigned the properties of different inclusion phases with the frequencies according to their Volume fractions. In the first case, the inclusion phases are isotropic. In the other case, the inclusions are anisotropic, their relative anisotropic orientations are random. The explicit upper and lower estimates for the effective conductivity and bulk modulus of such configurations are derived. (C) 1998 Elsevier Science Ltd.