Quasi-explicit time-integration schemes for dynamic fracture with set-valued cohesive zone models

We investigate quasi-explicit time-integration schemes for solving dynamic fracture problems with set-valued cohesive zone models. These schemes combine a central difference time-integration scheme and a partially implicit and lumped treatment of the cohesive forces. At each time step, the displacements of the nodes in the interior of the domain are computed in an explicit way, while the displacements of each node at the interface are computed by solving a local nonlinear problem. The method provides a general and robust way of treating the set-valued cohesive zone model while keeping a moderate computational cost.