X-FEM a good candidate for energy conservation in simulation of brittle dynamic crack propagation

Abstract

This paper is devoted to the simulation of dynamic brittle crack propagation in an isotropic medium. It focuses on cases where the crack deviates from a straight-line trajectory and goes through stop-and-restart stages. Our argument is that standard methods such as element deletion or remeshing, although easy to use and implement, are not robust tools for this type of simulation essentially because they do not enable one to assess local energy conservation. Standard cohesive zone models behave much better when the crack’s path is known in advance, but are difficult to use when the crack’s path is unknown. The simplest method which consists in placing the cohesive segments along the sides of the finite elements leads to crack trajectories which are mesh-sensitive. The adaptive cohesive element formulation, which adds new cohesive elements when the crack propagates, is shown to have the proper energy conservation properties during remeshing. We show that the X-FEM is a good candidate for the simulation of complex dynamic crack propagation. A two-dimensional version of the proposed X-FEM approach is validated against dynamic experiments on a brittle isotropic plate.