A new technique for the numerical solution of a class of integro-differential equations arising in elastodynamic crack propagation problems

Abstract

A strategy for the numerical solution of a type of integro-differential equation arising from the analysis of dynamic crack propagation problems is presented. Specifically, the problem of interest is that of a mode III crack dynamically propagating in a homogeneous linear elastic medium while the crack tip consists of a nonlinear rate-dependent cohesive (or failure) zone. The mode of propagation is general, that is, not restricted to steady-state or other special regimes. Furthermore, the presented solution technique is in no way restricted to mode III problems.