A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces

TLDR

Numerical simulations of crack initiation with cohesive zone laws are often halted by elastic snap‑back instabilities that prevent quasi‑static finite element convergence and block post‑instability analysis. This study demonstrates that adding a small viscosity to the cohesive interface constitutive equations eliminates these convergence problems. Guidelines for choosing appropriate viscosity values are derived from simple boundary‑value problems and illustrated by modeling crack nucleation at an elastic thin‑film/elastic‑plastic substrate interface under contact loading.

Abstract

Numerical simulations of crack initiation which use a cohesive zone law to model a weak interface in the solid are often limited by the occurrence of an elastic snap-back instability. At the point of instability, quasi-static finite element computations are unable to converge to an equilibrium solution, which usually terminates the calculation and makes it impossible to follow the post-instability behaviour. In this paper, we show that such numerical difficulties can easily be avoided by introducing a small viscosity in the constitutive equations for the cohesive interface. Simple boundary value problems are used to develop guidelines for selecting appropriate values of viscosity in numerical simulations involving crack nucleation and growth. As a representative application, we model crack nucleation at the interface between an elastic thin film and an elastic–plastic substrate, which is subjected to contact loading.