Constitutive relationships for composites are investigated in micromechanics. The stress tensor and the strain tensor are decomposed into two orthogonal complementary parts, viz the in-plane part and out-of-plane part, respectively. According to the fact that the in-plane part of strain tensor and the out-of-plane part of stress tensor are continuous across a perfect interface, continuity at a perfect interface between phases is rigorously satisfied, and the interactions between phases are correctly considered. Under these conditions the effective elastic tensor of an n-phase stratified media is analyzed as a whole. Furthermore, the analytical solutions of effective elastic properties of statistically transversely isotropic medium and statistically isotropic medium are obtained from the point of view of statistical averaging. The present theoretical results are in good agreement with related theoretical and experimental results for a two-phase alloy system WC-Co.
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