A stable P1∕P1 finite element for finite strain von Mises elasto-plasticity

The finite element P1∕P1 is well known for being unsuitable for the simulation of incompressible material flows. In von Mises elasto-plasticity, the volume changes can become negligible when the plastic strain grows higher than the elastic strain. Thus, the material flow is nearly incompressible even if a small volumic elastic strain persists. In this context, the finite element P1∕P1 leads to pressure oscillations which need to be addressed for achieving satisfactory solutions. The aim of this work is to propose a stabilized formulation without introducing new degrees of freedom or stabilization parameters as for sub-grid scale techniques. Unlike to the standard SUPG method, the stabilization depends on the time step. Examples show that a first order accuracy can be obtained for the pressure and the approach developed can be well suited for cyclic loadings.