Variational multiscale-stabilized extended B-spline-based mixed implicit material point method for elastoplasticity at finite strains

To further improve the accuracy of the extended B-spline-based implicit material point method (EBSMPM), this study extends the variational multiscale (VMS)-stabilized displacement-pressure (u-p) mixed formulation to elastoplasticity at finite strains. In large deformation analysis of elastoplastic materials, numerical instabilities such as volumetric locking and pressure oscillations may occur due to plastic deformations. To overcome these issues, we adopt the u-p mixed formulation that introduces pressure as an additional independent variable. The pressure constraint equation in the mixed formulation is generalized to be applicable to both pressure-independent and pressure-dependent plasticity models. To satisfy the stability condition for mixed formulation with equal-order interpolation, the variational multiscale (VMS) method is adopted for stabilization. The stabilization terms are derived in a manner consistent with the proposed mixed formulation and incorporated into the EBSMPM. Five numerical examples are conducted for two- and three-dimensional problems to demonstrate the performance of the proposed method in suppressing pressure oscillations as well as volumetric locking. The results confirmed that the proposed method effectively suppresses pressure oscillations and volumetric locking in pressure-independent elastoplastic materials and achieves similar effectiveness even for pressure-dependent elastoplastic materials by appropriately selecting stabilization parameters.