Micromechanical modeling of a cracked elliptically orthotropic medium

In this paper, we derive the second-order crack opening displacement tensor for an arbitrarily oriented elliptical in elliptically orthotropic (EO) matrix. This result is obtained explicit closed form. The approach based on Saint-Venant’s idea of linear transformation between boundary value problems and isotropic bodies. solution utilizes classical representation ellipsoid where smallest aspect ratio approaches zero Taylor expansion corresponding Hill tensor. It shown, particular, that transformed cracks have neither same in-plane nor vanishing ratio. requires a correction factor Some specific relative orientations with respect to symmetry planes EO matrix are considered detail effective properties calculated case randomly distributed cracks. also extended cylindrical (plane strain) crack.