a b s t r a c tSeveral published papers deal with the possibility of replacing a damage finite element model by a combination of cohesive zones and finite elements. The focus of the paper is to show under which conditions this change of model can be done in an energy-wise manner.The objective is to build a cohesive model based on a known damage model, without making any assumption on the shape of the cohesive law. The method is characterized, on the one hand, by the use of a well-defined thermodynamic framework for the cohesive model and, on the other hand, by the idea that the main quantity which must be maintained through the change of model is the energy dissipated by the structure. An analysis of the stability criteria enables us to determine the domains of validity of the different models. Thus, we show that it is consistent to derive the cohesive law from a given nonlocal damage model because the occurrence of a discontinuity can be viewed as an alternative way to limit localization. The method is illustrated on one-dimensional examples and a numerical resolution method for the problem with a cohesive zone is presented.

SUMMARYThis paper provides a comparison between one particular phase-field damage model and a thick level set (TLS) damage model for the simulation of brittle and quasi-brittle fractures. The TLS model is recasted in a variational framework, which allows comparison with the phase-field model. Using this framework, both the equilibrium equations and the damage evolution laws are guided by the initial choice of the potential energy. The potentials of the phase-field model and of the TLS model are quite different. TLS potential enforces a priori a bound on damage gradient whereas the phase-field potential does not. The TLS damage model is defined such that the damage profile fits to the one of the phase-field model for a beam of infinite length. The model parameters are calibrated to obtain the same surface fracture energy. Numerical results are provided for unidimensional and bidimensional tests for both models. Qualitatively, similar results are observed, although TLS model is observed to be less sensible to boundary conditions.