A numerical solution technique for a class of integro-differential equations 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.