A mixed element method in gradient plasticity for pressure dependent materials and modelling of strain localization Original Research Article

This paper presents a mixed strain element method in gradient plasticity for pressure dependent materials at large strains and its application to the modelling of strain localization. The two yield strength parameters of strain hardening/softening materials not only depend on the internal state variable but also on its Laplacian. The evaluation of the Laplacian is based on a least square polynomial approximation of the internal state variable around each integration point. The present non-local approach allows to satisfy exactly the consistency condition in a pointwise fashion but in the non-local sense and at each iteration of a load step. To derive the consistent element formulations in the context of mixed finite element with one point quadrature and hourglass control and the non-local pressure dependent elasto-plasticity, a natural coordinate system in the stress space and a new definition of internal state variable are introduced. The capability of the present approach to preserve ellipticity as strain softening behaviour is incorporated into a computational model is demonstrated by the numerical results, which illustrate that pathological mesh dependence has been overcome.