Hourglass control for Smooth Particle Hydrodynamics removes tensile and rank-deficiency instabilities

We present a stabilization scheme for elastoplastic Smooth-Particle Hydrodynamics (SPH) which overcomes two major challenges: (i) the tensile instability inherent to the updated Lagrangian approach is suppressed and (ii) the rank-deficiency instability inherent to the nodal integration approach is cured. To achieve these goals, lessons learned from the Finite-Element Method are transferred to SPH. In particular, an analogue of hourglass control is derived for SPH, which locally linearizes the deformation field to obtain stable and accurate solutions, without the need to resort to stabilization via excessive artificial viscosity. The resulting SPH scheme combines the ability of updated Lagrangian SPH to model truly large deformations with the accuracy and stability needed to faithfully perform simulations. This claim is supported by the analysis of problematic cases and the simulation of an impact scenario.