A finite element approach coupling a continuous gradient damage model and a cohesive zone model within the framework of quasi-brittle failure

A coupled continuous/discontinuous approach involving a gradient damage model and a cohesive zone model is proposed to simulate crack propagation in quasi-brittle materials. First, a semi analytical one-dimensional study is carried out on a bar submitted to tensile loading (in the case of inhomogeneous symmetrical damage localisation) in order to identify a set of cohesive laws allowing to switch from damage growth to cohesive crack opening. This continuous/discontinuous approach is constructed so that energetic equivalence between both models remains ensured whatever the damage level reached when switching. This strategy is then extended to the finite element framework, in the case of 2D (and 3D) crack propagation under mode I loading conditions. Both non local and cohesive models are combined using a critical damage criterion which is checked at the end of each converged time step.