Stress concentration at irregular surfaces of anisotropic half-spaces

Summary

An analytical method is presented to derive the stresses in anisotropic half-spaces with smooth and irregular surface morphologies. The half spaces can be subjected to body forces, surface tractions, and uniform far-field stresses. The general solution is expressed in terms of three analytical functions using the analytical function method of anisotropic elasticity. These three functions are then determined using a numerical conformal mapping technique and an integral equation method. Numerical examples are presented for the stress concentration at irregular surfaces induced by a uniform far-field horizontal stress. The elastic half-spaces are assumed to be transversely isotropic or isotropic, and their surface morphologies are constructed by the superposition of multiple long and symmetric ridges (mounds) and valleys (depressions). For isotropic media, the stress concentration depends only on the half-space surface geometry. It is found here that for anisotropic media, the half-space surface geometry, as well as the orientation of the planes of material anisotropy, have a great effect on the stress concentration. The degree of material anisotropy, on the other hand, has little influence on the stress concentration.