Integral equations for 2D and 3D problems of the sliding interface crack between elastic and rigid bodies

Abstract

This paper revisits the sliding interface crack problem between elastic and rigid half-planes studied by Bui and Oueslati and provides an alternative method of derivation of the solution, which will then be extended to three-dimensional (3D) crack problems. Based upon the displacement continuation technique of complex potentials, an appropriate Green function for the isolated edge dislocation dipole at the interface is given. Then by considering the sliding condition along the interface crack, the field equations can be obtained for the two-dimensional (2D) problem. Furthermore, it is shown that the edge dislocation dipole in 2D appears to be a particular form of the fundamental Kupradze–Basheleishvili tensor in 3D, which provides a method for deriving the coupled nonlinear integral equations for the same frictional interface plane crack of an arbitrary shape. The present work describes how the 3D sliding interface crack is related to the same problem in 2D.