Total Deformation-based MPM for Perfectly Elastic Solid Simulation with Strong Deformations

We present a new MPM-based solver for perfectly elastic solids, which can recover from strong deformations and naturally allows contact handling. Typical MPM solvers suffer from numerical fracture, where objects break apart even when no plasticity is included in the elasticity model. Previous approaches for perfectly elastic solids solve this by computing forces on a fixed grid in the reference configuration. However, this makes them incompatible with standard collision handling methods. We instead propose a method for deformable solid simulation without numerical fracture, that still computes elastic forces on the current grid. Our method can easily include grid-based collision handling, as commonly used in MPM frameworks. Additionally, we compute the deformation directly from the particle positions and a fixed reference grid, without any updates based on velocity gradients. This facilitates the inclusion of particle-level collision handling and zero-energy mode suppression, which counteracts artifacts from non-linear deformations. As a result, we can efficiently simulate complex scenarios of elastic objects undergoing large deformations, including contact.