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

• A non-local damage model is enriched with displacement jumps (i.e. cracks).
• Cohesive cracks propagate through the regularised damage bulk.
• Energy not dissipated by the bulk is estimated accurately and transferred to the crack.
• The proposed model and the reference continuous model are energetically equivalent.

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<1Dcrit<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.