Peridynamics versus XFEM: a comparative study for quasi-static crack problems

Peridynamics (PD) is a nonlocal continuum theory based on integro-differential equations without spatial derivatives. The fracture criterion is implicitly incorporated in the PD theory and fracture is a natural outcome of the simulation. However, capturing of complex mixed-mode crack patterns has been proven to be difficult with PD. On the other hand, the extended finite element method (XFEM) is one of the most popular methods for fracture which allows crack propagation with minimal remeshing. It requires a fracture criterion which is independent of the underlying discretization though a certain refinement is needed in order to obtain suitable results. This article presents a comparative study between XFEM and PD. Therefore, two examples are studied. The first example is crack propagation in a double notched specimen under uniaxial tension with different crack spacings in loading direction. The second example is the specimens with two center cracks. The results show that PD as well as XFEM are well suited to capture this type of behaviour.