Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture

Adaptive mesh refinement and coarsening schemes are proposed for efficient computational simulation of dynamic cohesive fracture. The adaptive mesh refinement consists of a sequence of edge-split operators, whereas the adaptive mesh coarsening is based on a sequence of vertex-removal (or edge-collapse) operators. Nodal perturbation and edge-swap operators are also employed around the crack tip region to improve crack geometry representation, and cohesive surface elements are adaptively inserted whenever and wherever they are needed by means of an extrinsic cohesive zone model approach. Such adaptive mesh modification eventsare maintained in conjunction with a topological data structure (TopS). The so-called PPR potential-based cohesive model (J. Mech. Phys. Solids 2009; 57:891-908) is utilized for the constitutive relationship of the cohesive zone model. The examples investigated include mode I fracture, mixed-mode fracture and crack branching problems. The computational results using mesh adaptivity (refinement and coarsening) are consistent with the results using uniform mesh refinement. The present approach significantly reduces computational cost while exhibiting a multiscale effect that captures both global macro-crack and local micro-cracks.