Approaches to dynamic fracture modelling at finite deformations

The focus of the present paper is on the finite element modelling of dynamic fracture based on the concept of locally enriched element shape functions in the vicinity of the crack, in line with the eXtended Finite Element Method (X-FEM). For this purpose, the proper governing equations for the case of a propagating crack within a hyperelastic material is established, including the definition of the concept of material motion which kinematically describes the progression of the crack. Furthermore, two different approaches to describe the material degradation and separation are proposed. The first approach, denoted the material crack driving force model, is based on the concept of material (or configurational) forces associated with the material motion. The basic motivation is that, in this context, a driving force is identified at the crack tip, which points in the direction of maximum energy release upon crack propagation. An additional interesting feature of this force is that the projection in the crack propagation direction corresponds to the energy released for such a propagation, whereby an intuitive criterion for crack propagation based on the direction and magnitude of this force is proposed. The second approach is based on the classical cohesive zone concept, extended to include rate effects to capture experimentally observed phenomena such as growing process zones during propagation as well as limited crack propagation speeds well below the theoretical limit. Both models are investigated and compared in a couple of numerical examples in the latter part of the paper, showing both the predictive capabilities as well as some limitations of the two approaches. It has also been shown that, for a specific set of parameters, the two models can reproduce (almost) the same response.