Calculation of interfacial stresses in composites containing elliptical inclusions of various types

• A volume integral equation method was used for plane strain elastostatic problems.
• An infinite isotropic solid containing multiple elliptical inclusions was considered.
• Interfacial stresses between the matrix and the central inclusion were calculated.
• Values for number, concentration, packing and aspect ratio of inclusions were varied.
• The orientation angles of multiple anisotropic elliptical inclusions were arbitrary.

A volume integral equation method (VIEM) is used to study elastostatic problems in an unbounded elastic solid containing multiple elliptical inclusions of arbitrary orientation subject to uniform tensile stress at infinity. The inclusions are assumed to be long parallel elliptical cylinders composed of isotropic or anisotropic elastic materials and perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinders. In contrast to previous studies cited in this paper where only one or a few specific types of inclusions were considered, a detailed analysis of the stress field at the matrix-inclusion interface for square and hexagonal packing arrays is carried out herein, taking into account different values for the number, aspect ratio, orientation angle and concentration of the elliptical inclusions. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and finite element methods.