Uniform asymptotic solutions for lamellar inhomogeneities in anisotropic elastic solids

We consider the problem of a lamellar anisotropic inhomogeneity of arbitrar y shape embedded in a different anisotropic matrix of infinite extent. Unif orm asymptotic solutions for the equations of elastostatics on this configu ration are obtained. The first order terms, in the inhomogeneity thickness, are explicitly determined for elastic inclusions, rigid inclusions, or cra cks. We give real-form expressions for displacements and stresses at the in terface and on the inhomogeneity axis. For the particular case of an ellipt ic 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, wh ereas for elliptic inclusions these stresses become unbounded at the inclus ion's ends, for a lemon-shaped inclusion they remain bounded.