An implicit non-local damage to crack transition framework for ductile materials involving a cohesive band model

Accurate numerical predictions of the entire ductile failure process is still challenging. There are two main philosophies to model the process consisting in an initial diffuse stage followed by localised crack initiations and propagations. On the one hand, discontinuous approaches are adapted to localised processes as crack propagation but fail in capturing diffuse damage evolution. Moreover, they do not usually capture stress triaxiality effects, required for accurate ductile failure simulations. On the other hand, continuum damage models are suited for diffuse damage modelling but are unable to represent properly physical discontinuities.

In order to describe the entire ductile failure process, the numerical scheme proposed here combines both approaches through a mesh-independent implicit non-local damage model combined with a cohesive band model, an extrinsic cohesive law, in a discontinuous Galerkin finite element framework. By assuming that all the damaging process is concentrated inside a band of small but finite thickness ahead of the crack surface, the cohesive forces are computed from neighbouring strains and the cohesive jump using an appropriate damage model. By this way, this approach naturally incorporates stress triaxiality effects. It has successfully been applied in the case of elastic damage for which the band thickness was evaluated to ensure the energetic consistency of the damage to crack transition with respect to purely non-local continuum damage mechanics [1]. In the present work, the scheme is extended to the case of non-local porous-plastic damage Gurson model accounting for large shear effects. A crack is introduced at the transition corresponding to intensive plastic localisation or void coalescence predicted by the Thomason model.

[1] Leclerc J., Cohesive band model: a cohesive model with triaxiality for crack transition in a coupled non-local implicit discontinuous Galerkin/extrinsic cohesive law framework. Int. J. Num. Meth. Eng. (2017).