A mixed stabilized MPM formulation for incompressible hyperelastic materials using Variational Subgrid-Scales

The Material Point Method (MPM) stands as a continuum-based particle technique designed for addressing large deformation problems. However, the treatment of incompressible materials using MPM remains underexplored. This study focuses on adapting established techniques from the Finite Element Method (FEM) to address incompressibility within MPM for dynamic hyperelastic problems. Firstly, we introduce a mixed displacement-pressure formulation to tackle incompressibility. Secondly, we employ two different stabilization techniques rooted in the Variational Multiscale Method (VMS) to enable the utilization of equivalent low-order spaces for approximating both primary unknowns. The efficacy of these formulations is compared with alternative stabilization techniques and validated across various two- and three-dimensional benchmark problems to assess its accuracy and robustness.