Wave propagation in the presence of empty cracks in an elastic medium

Abstract

Abstract This paper proposes the use of a traction boundary element method (TBEM) to evaluate 3D wave propagation in unbounded elastic media containing cracks whose geometry does not change along one direction. The proposed formulation is developed in the frequency domain and handles the thin-body difficulty presented by the classical boundary element method (BEM). The empty crack may have any geometry and orientation and may even exhibit null thickness. Implementing this model yields hypersingular integrals, which are evaluated here analytically, thereby surmounting one of the drawbacks of this formulation. The TBEM formulation enables the crack to be modelled as a single line, allowing the computation of displacement jumps in the opposing sides of the crack. Furthermore, if this formulation is combined with the classical BEM formulation the displacements in the opposing sides of the crack can be computed by modelling the crack as a closed empty thin body.