Energy minimization versus criteria-based methods in discrete cohesive fracture simulations

We highlight the ability of a proposed energy-based cohesive interface method to produce stable and convergent solutions where methods based on failure criteria at similar discretization levels fail. The key feature of the method is the smooth transition from “uncracked” to “cracked” states, i.e., internal forces remain continuous functions of the deformation at initiation of failure. This property is missing in methods based on stress criteria. In explicit time stepping calculations, lack of continuity gives rise to spurious crack opening velocity fields. This issue is particularly significant in multiphysics problems such as hydraulic fracturing due to the coupling of the unknown fields and may lead to instability of the computational algorithm. In implicit time stepping calculations, lack of continuity introduces challenges in obtaining convergence of Newton iterations. Often the issue is circumvented by keeping cracks fixed within the iterative solver; the configuration of cracks is only updated at the end of a time step in such algorithms. This approach leads to the dependence of the crack-tip velocity on temporal and spatial discretization parameters. We present various simulation results to show that the energy approach is free of all such undesirable behaviors.