Analysis for Isotropic Elastic Medium with Multi-Layered Elliptic Inclusions under Out-of-Plane Normal Stress

Abstract

In this paper, an analytical solution for infinite medium containing elliptical inclusions under uniform out-of-plane normal stress is presented. It is assumed that each layer consists of isotropic elastic material, and that all elliptic boundaries have common focal point. Introducing such assumptions, prescribed solution is obtained to apply the concept of two-dimensional elastic theory. Because only a normal stress whose direction is parallel to a generator of elliptical inclusion affects a matrix, it is noted that antiplane shear stresses do not occur on every points of analytical model. Some numerical examples are shown in graphic and tabular representations.