A method for modeling the transition of weak discontinuities to strong discontinuities: from interfaces to cracks

Cohesive zone models are widely used to model interface debonding problems; however, these models engender some significant drawbacks, including the need for a conforming mesh to delimit the interfaces between different materials or components and that penalty or other constraint methods necessary to enforce initially perfect adhesion at interfaces degrade the critical time step for stability in explicit time integration. This article proposes a new technique based on the extended finite element method that alleviates these shortcomings by representing the transition from perfect interfacial adhesion to debonding by switching the enriched approximation basis functions from weakly discontinuous to strongly discontinuous. At this transition, the newly activated degrees of freedom are initialized to satisfy a point-wise consistency condition at the interface for both displacement and velocity. Analysis of the stable time step for one-dimensional elements with mass lumping is presented, which shows the increase of the stable time step compared with a cohesive zone model. Both one-dimensional and two-dimensional verification examples are presented, illustrating the potential of this new approach.