On effective moduli of inhomogeneous media characterized by several small parameters

Composites and porous media of elongated structure, as well as materials with pores or inclusions having the shape of parallelepipeds or channels of rectangular cross-section, are considered under certain conditions on the inclusion-to-matrix modulus ratio and the volume fraction of inclusions (pores). The effective moduli are calculated by the method of mathematical homogenization theory. Numerical results on the dependence of the effective moduli on the prolateness of the structure, the shape of the inclusions (pores), the inclusion-to-matrix modulus ratio, and the volume fraction of inclusions (pores) are given. The effective moduli computed according to the algorithm of mathematical homogenization theory are compared with those given by the explicit approximate formulas earlier developed by the authors.