A thermodynamic method for the construction of a cohesive law from a nonlocal damage model

Abstract

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.

Elastic damage to crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework

“…First the theoretical background of both the CZM and the implicit non-local CDM are briefly summarized. Then the main results developed in [35,36,37] to derive the equivalence between the energy dissipated with both models are given. Based on this we construct a TSL in the particular case of the scalar elastic damage model expressed in a 1D implicit gradient setting.…”

“…In this paper we consider the implicit non-local formulation developed in [5,6] for a scalar damage model under the assumption of isotropic damage. Although this model remains simplistic it has been widely studied in the literature, including to consider the damage to crack transition [36,37], and calibrated experimentally for short glass-fiber reinforced polymers [6], which allows the application presented later on to be validated. In a future work it is intended to consider more complex (elasto-plastic) damage models.…”

“…In this part, the main results developed in [35,36,37] are first recalled in a general case, before being particularized to a 1D problem. This 1D solution is then exploited to construct the TSL upon transition from a CDM to a CZM providing this transition occurs after the strain softening onset.…”

“…The CZM is integrated in the hybrid DG/ECL to model the discontinuous stage. Finally, upon damage to crack transition, the TSL of the CZM is defined to respect the equivalence between the fracture energy of the non-local damage and cohesive crack following the work in [35,36,37]. Note that this theoretical framework has already been used for brittle materials to define the transition from a non-local implicit CDM to a CZM embedded in the XFEM method [38] and the transition from a gradient enhanced damage model to an intrinsic cohesive crack in a predefined direction (mode I) [39].…”

“…In Section 2 the theoretical formalism to construct a TSL from a CDM when a transition has been decided is developed based on the existing theoretical background of energetic equivalence between the two concepts [35,36,37]. We also propose a transition criterion based on the effective stress state, which avoids elements blow-up during the numerical simulation.…”