The Green's Function BEM for Bimaterial Solids Applied to Edge Stress Concentration Problems

Abstract

A boundary element method (BEM) for bimaterial domains consisting of two isotropic solids bonded perfectly along the straight interface will be developed. We follow the physical interpretation of Somigliana’s identity to represent the displacement in the bimaterial domain by the continuous distributions of the line forces and dislocation dipoles over its boundary. The fundamental solutions used are the Green’s functions for the line force and the dislocation dipole that satisfy the traction and displacement continuity across the interface of two domains. There is no need to model the interface because the required continuity conditions there are automatically satisfied by the Green’s functions. The BEM will be applied to study the edge stress concentration of the bimaterial solids. We calculate the singular stress distribution at the free edge of the interface for various bimaterial configurations and loadings, in particular, for the domain consisting of thin coating over the substratum. Since the Green's function BEM does not require the boundary elements on the interface, it can handle the edge singularity on the interface accurately even for extremely thin coatings. The BEM developed here is not limited to the edge stress concentration problems and can be applied to a broad range of the bimaterial domain problems effectively.