Uniform stress field inside an anisotropic non-elliptical inhomogeneity interacting with a screw dislocation

We find that an anisotropic non-elliptical inhomogeneity interacting with a screw dislocation in a matrix subjected to remote uniform stresses and anti-plane shear deformations may still admit an internal uniform stress field. Our analysis indicates that the screw dislocation does not affect the uniform stresses inside the inhomogeneity but does play a crucial role in determining the shape of the inhomogeneity. In fact, we find that the influence of the screw dislocation gives rise to the possibility that the boundary of the inhomogeneity may have up to three sharp corners. Our discussion extends to the case when multiple screw dislocations interact with the non-elliptical inhomogeneity leading to a conjecture concerning the maximum allowable number of sharp corners in an inhomogeneity with Eshelby's uniformity property.