Multiple elliptical inclusions of arbitrary orientation in composites

A volume integral equation method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing multiple elliptical inclusions of arbitrary orientation subjected to uniform tensile stress at infinity. The inclusions are assumed to be long parallel elliptical cylinders composed of isotropic and anisotropic elastic material perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinders. A detailed analysis of the stress field at the matrix–inclusion interface for square and hexagonal packing arrays is carried out, taking into account different values for the number, orientation angles and concentration of the elliptical inclusions. The accuracy and efficiency of the method are examined in comparison with results available in the literature.