Non-hypersingular boundary integral equations for 3-D non-planar crack dynamics

Abstract

We derive a non-hypersingular boundary integral equation, in a fully explicit form, for the time-domain analysis of the dynamics of a 3-D non-planar crack, located in an infinite homogeneous isotropic medium. The hypersingularities, existent in the more straightforward expression, are removed by way of a technique of regularization based on integration by parts. The variables are denoted in terms of a local Cartesian coordinate system, one of the axes of which is always held locally perpendicular to the potentially curved surface of the crack. Also given, in a fully explicit form, are the expressions for the off-fault stress and displacement field, as well as the special form of the equations for the case in which the fault is planar.