Elastic Stress Concentration of an Ellipsoidal Inclusion of Revolution in the Vicinity of a Bimaterial Interface

摘要

This paper deals with a stress concentration problem of an ellipsoidal inclusion of revolution in a bimaterial body under tension. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r and z-directions in bimaterial bodies having the same elastic constants of those of the given problem. In order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in the previous paper are used. Then the body force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries of both the matrix and inclusion even when the inclusion is very close to the bimaterial interface. Then, the effect of bimaterial interface on the stress concentration factor is discussed with varying the distance from, the interface, shape ratio, and elastic ratio.