Stress state of an anisotropic body with smooth curvilinear inclusions and cracks under antiplane deformation

The antiplane problem of the theory of elasticity for an anisotropic body with smooth curvilinear anisotropic inclusions and cracks was solved using the method of singular integral equations. For one elliptic inclusion and an arbitrarily oriented rectilinear crack in the orthotropic plane, the obtained system of the integral first and second order equations is numerically solved by the quadrature method. The dependences of the stress intensity factors at the crack tips on the geometric parameters of the problem and the elastic constants of orthotropic materials of the matrix and inclusion are constructed.