[en] Fracture mechanical problems can be solved by coupling the finite elements with a cohesive approach. Unfortunately, the classical cohesive methods suffer from severe limitations. Indeed, on one hand, the intrinsic approach, which inserts the cohesive elements at the beginning, has to model the prefracture stage. This requires an initial slope in the traction separation law that should tend toward infinity to avoid lack of consistency leading to obvious numerical problems. On the other hand, the extrinsic cohesive method inserts the cohesive elements during the simulation when a fracture criterion is reached. This insertion requires topological mesh modifications and therefore a very complicated implementation, especially in a parallel code.
To overcome these limitations, new methods were developed and in particular, an approach based on discontinuous Galerkin formulation (DG) has been pioneered by R. Radovitzky (Radovitzky cmame2011). The use of the DG principle allows to formulate the problem with discontinuous elements and the continuity between them is ensured weakly by terms integrated on the elements interface . These interface elements can be easily replaced by a cohesive element during the simulation.
We have recently developed this approach for shells (Becker cmame2011) to obtain a full DG method. Moreover, a new cohesive law based on the reduced stresses of the thin bodies formulation is developed to propagate a fracture through the thickness. This cohesive model dissipates the right amount of energy during crack phenomena. These developments are implemented in parallel and validated by the study the blast of a notched cylinder, for which experimental and numerical (by XFEM method) data are reported in the literature by R. Larsson (Larsson ijnme2011).
Finally, as thin structures are often made of ductile materials, which show large deformations before fracture, the formulation is extended to the non linear case with hyperelastic material law. This one can take into account the damage and a criterion based on the work of Huespe (Huespe plasticity2009) is developed to localize the damage leading to the apparition and propagation of cracks.
