Dynamically accelerating cracks part 2: a finite length mode III crack in elastic material

Abstract

We consider a dynamically accelerating, finite length, mode III crack in an infinite elastic body. This initial boundary value problem has the nature of a free boundary problem since the crack tip motion is a priori unknown and must be found as part of the solution after imposition of a fracture criterion. Using an analog to a Dirichlet-to-Neumann map, we reduce the fracture problem to integrodifferential equations along the boundary that, for simplicity, we combine with a stress intensity factor fracture criterion. This approach has the advantage of being applicable to cases of multiple cracks as well as, in principle, to mode I cracks and to cracks in viscoelastic materials.