Displacement field in an elastic solid with mode-III crack and first-order surface effects

Abstract

We analyze a nonstandard boundary-value problem for Laplace's equation characterizing the displacement field arising from the antiplane deformations of an infinite elastic solid containing a sharp finite crack when first-order surface effects are included on the crack faces. The surface effects are incorporated using the continuum-based surface/interface model of Gurtin and Murdoch. We establish a uniqueness result for the displacement field and use complex variable methods to reduce the problem to a series of integral equations which are solved numerically using an efficient, stable, yet convenient finite element discretization method. Our results demonstrate the effect of the surface on the displacement field and its implications for the corresponding stress distributions in the vicinity of the crack.