Integral equations of a cohesive zone model for history-dependent materials and their numerical solution

Abstract

A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for computing the evolution of the crack and CZ in time is discussed along with some numerical results.