A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous Galerkin‐cohesive band model framework

Abstract

SummaryModelling the entire ductile fracture process remains a challenge. On the one hand, continuous damage models succeed in capturing the initial diffuse damage stage but are not able to represent discontinuities or cracks. On the other hand, discontinuous methods, as the cohesive zones, which model the crack propagation behaviour, are suited to represent the localised damaging process. However, they are unable to represent diffuse damage. Moreover, most of the cohesive models do not capture triaxiality effect. In this paper, the advantages of the two approaches are combined in a single damage to crack transition framework. In a small deformation setting, a nonlocal elastic damage model is associated with a cohesive model in a discontinuous Galerkin finite element framework. A cohesive band model is used to naturally introduce a triaxiality‐dependent behaviour inside the cohesive law. Practically, a numerical thickness is introduced to recover a 3D state, mandatory to incorporate the in‐plane stretch effects. This thickness is evaluated to ensure the energy consistency of the method and is not a new numerical parameter. The traction‐separation law is then built from the underlying damage model. The method is numerically shown to capture the stress triaxiality effect on the crack initiation and propagation.