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 an-isotropic 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.
