Cracking Cohesive Law Thermodynamically Equivalent to a Non-Local Damage Model

This paper deals with the transition from a localized damage state to crack formation. Several attempts have already been made in this field. Our approach is in the continuity of studies where thermodynamic considerations lead to the definition of an equivalent crack concept. The main idea consists in replacing a damaged localized zone by a crack in order to recover the same amount of dissipated energy. On the one hand, a nonlocal model is used to modelize accurately localized damage. On the other hand, an elastic model which authorizes the formation of a crack described by a cohesive zone model is used. This cohesive zone model is defined thermodynamically in order to be in concordance with the damage model. The method allows obtaining the cohesive zone model traction curve from the knowledge of the nonlocal damage model solution. The numerical implementation is done using a Lagrangian multiplier that ensures the energetic equivalence between both models.