Phase-field regularised cohesive zone model for interface modelling

A discrete interface is represented as a smeared interface in the framework of phase field regularisation. Due to the numerical challenge when imposing boundary conditions we prescribe the phase field in the domain using analytical solutions. We obtain the displacement and the strain from the variational form of the energy functional, but also in the framework of the regularised extended finite element method. Indeed, both approaches result in identical forms, validating the rigour of the method. We have examined different forms of the phase field model and conclude that models with a compact support are more appropriate for modelling interfaces. The method combines advantages of discrete and smeared approaches. Compared to discrete interface models, the method holds similar properties as the extended finite element method (XFEM): no need to treat cracks as geometric discontinuities and avoiding mesh refinement around crack tips. Different from the XFEM, however, the method does not introduce enrichment functions to describe cracks. An advantage compared to the phase field method is that this method directly employs the cohesive zone law from the discrete model, which is physically relevant. The accuracy of the approach for cohesive interface modelling is demonstrated by several numerical examples, including a bar, an L-shaped specimen, and a fibre embedded in an epoxy matrix.