Wave propagation in the presence of empty cracks in elastic slabs -- TBEM and MFS Formulations

Abstract

Summary This paper evaluates the 3D wave propagation in an elastic slab containing cracks whose geometry does not change along the direction parallel to the formation surfaces. Two different formulations are used and compared: the Traction Boundary Element Method (TBEM) and the Method of Fundamental Solutions (MFS). Both approaches are developed in the frequency domain and surmount the thin-body difficulty posed by the classical Boundary Element Method (BEM). The TBEM models the crack as a single line. The resulting hypersingular integrals are evaluated analytically. For the MFS, the solution is approximated in terms of a linear combination of fundamental solutions, generated by a set of virtual sources that simulate the scattered field produced by the crack. A domain decomposition technique avoids the use of any enriched function to model displacement jumps across the crack.