Uniformity of stresses inside an anisotropic elliptical inhomogeneity with an imperfect interface

By employing the Stroh formalism for two-dimensional anisotropic elasticity, we find that a uniform stress field exists inside an anisotropic elliptical inhomogeneity imperfectly bonded to an infinite anisotropic matrix subject to uniform stresses and strains at infinity.Here, the behavior of the imperfect interface between the inhomogeneity and the matrix is characterized by the linear spring model with vanishing thickness.The degree of imperfections, both normal and in-plane tangential to the interface, are assumed to be equal.A particular form of the interface function that leads to a uniform stress field within the anisotropic elliptical inhomogeneity is identified.Also presented are real form expressions for the stress field inside the inhomogeneity that are shown to be valid for mathematically degenerate (isotropic) material as well.We note that the interpenetration issue that arises from application of the linear spring model to the imperfect interface is not discussed here.