Green’s functions for a bi-material problem with interfacial elliptical rigid inclusion and applications to crack and thin rigid line problems

Abstract

The Green’s functions for a point force and dislocation interacting with interfacial elliptical rigid inclusion in a bonded bi-material system are obtained by applying complex variable method and conformal mapping technique. The problem of an internal crack or thin rigid line interacting with the interfacial inclusion is then examined. For mapping the half plane with a semi-elliptic notch a rational mapping function is used. This helps in evaluating certain contour integrals quite easily. The Green’s function solutions are then used to simulate internal cracks or thin rigid lines to study their behavior in the presence of interfacial inclusion. Some interesting observations pertaining to the interaction between rigid inclusion and crack as well as between rigid inclusion and thin rigid line are discussed. In particular, stress intensity factors (SIF) at the tips of internal crack or stress singularity coefficients (SSC) at the tips of thin rigid line exhibit markedly different behavior depending on loading direction and distance between interfacial inclusion and crack (thin rigid line).