Uniform Asymptotic Solutions for Lamellar Inhomogeneities in Anisotropic Elastic Solids

Abstract

We consider the problem of a lamellar anisotropic inhomogeneity of arbitrary shape embedded in a different anisotropic matrix of infinite extent. Uniform asymptotic solutions for the equations of elastostatics on this configuration are obtained. The first order terms, in the inhomogeneity thickness, are explicitly determined for elastic inclusions, rigid inclusions, or cracks. We give real-form expressions for displacements and stresses at the interface and on the inhomogeneity axis. For the particular case of an elliptic inclusion or crack, our solution agrees with the asymptotic form of the exact solution. We also calculate the first order solution for lemon-shaped inhomogeneities and the corresponding expressions of the displacements and stresses on the interface and the inhomogeneity axis, and we find that, whereas for elliptic inclusions these stresses become unbounded at the inclusion's ends, for a lemon-shaped inclusion they remain bounded.