On the Anisotropic Elastic Inclusions in Plane Elastostatics

Abstract

By combining the method of Stroh’s formalism, the concept of perturbation, the technique of conformal mapping and the method of analytical continuation, a general analytical solution for the elliptical anisotropic elastic inclusions embedded in an infinite anisotropic matrix subjected to an arbitrary loading has been obtained in this paper. The inclusion as well as the matrix are of general anisotropic elastic materials which do not imply any material symmetry. The special cases when the inclusion is rigid or a hole are also studied. The arbitrary loadings include in-plane and antiplane loadings. The shapes of ellipses cover the lines or circles when the minor axis is taken to be zero or equal to the major axis. The solutions of the stresses and deformations in the entire domain are expressed in complex matrix notation. Simplified results are provided for the interfacial stresses along the inclusion boundary. Some interesting examples are solved explicitly, such as point forces or dislocations in the matrix and uniform loadings at infinity. Since the general solutions have not been found in the literature, comparison is made with some special cases of which the analytical solutions exist, which shows that our results are exact and universal.