A 3D locking-free XFEM formulation for the von Mises elasto-plastic analysis of cracks

The aim of this paper is to propose a mixed XFEM approach for the elasto-plastic analysis of cracks in compressible solid metals. The formulation proposed is capable of taking into account the plastic incompressibility induced by the von Mises yield criterion without leading to a volumetric locking phenomenon in 3D. The numerical formulation is regularized without adding parameters to be calibrated or adding equations to be solved as for the subgrid scale methods. The mixed XFEM technique developed has the benefit not to require special care for the numerical integration: hundreds of integration points can be used for integrating the asymptotic enrichment functions into each finite element. Examples are presented to show the relevance, the convergence and the efficiency of the new numerical formulation proposed in the case of linear and quadratic meshes.