Antiplane Strain Problems of an Elliptic Inclusion in an Anisotropic Medium

The antiplane strain problem of an elliptic inclusion in an anisotropic medium with one plane of symmetry is solved. Explicit expressions of compact form are obtained for the elastic field inside the inclusion, the stress at the boundary, and the strain energy of the system. The perturbation of an otherwise uniform stress field due to an elliptic inhomogeneity is studied, and explicit solutions are given for the extreme cases of an elliptic cavity and a rigid elliptic inhomogeneity. It is found that both the stress magnification at the edge of the inhomogeneity and the increase of strain energy depend only on the component $P23A$ of the applied stress for an elongated cavity; and depend only on the component $E13A$ of the applied strain for a rigid line inhomogeneity.