Green’s Function of a Bimaterial Problem With a Cavity on the Interface—Part I: Theory

Abstract

The problem of a point dislocation interacting with an elliptical hole located on a bimaterial interface is examined. Analytical solution is obtained by employing the techniques of complex variables and conformal mapping. A rational mapping function is used to map a half-plane with a semielliptical notch onto a unit circle. In the first part of this paper, complex potentials for the bimaterial system with an elliptical hole on the interface is derived when a point dislocation is present in the upper half-plane without loss of generality. The solution derived can be used as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.