A new continuous-discontinuous damage model: cohesive cracks via an accurate energy-transfer process

A new continuous-discontinuous strategy to describe failure of quasi-brittle materials is presented. For the early stages of the failure process, a gradient-enhanced model based on smoothed displacements is employed. As soon as the damage parameter exceeds a critical value Dcrit<1, a cohesive crack is introduced. A new criterion to estimate the energy not yet dissipated by the bulk when switching models-from continuous to continuous-discontinuous-is proposed. Then, this energy is transferred to the cohesive crack thus ensuring that the continuous and the continuous-discontinuous strategies are energetically equivalent. Compared to other existing techniques, this new strategy accounts for the different unloading branches of damage models and thus, a more accurate estimation of the energy that has to be transferred is obtained. The performance of this technique is illustrated with one- and two-dimensional examples.