Mastering Multi-State Dynamics: Continuum Damage and Viscoplastic MPM for RL-Based Dexterous Manipulation

Robotic manipulation of multi-state materials needs a simulator that handles large deformation, topology change, and two-way contact between tools and materials while staying fast enough to drive online reinforcement learning. We present MG-CD-MPM, a tool-centered localized extension of CD-MPM. The implicit Ginzburg-Landau phase-field damage system is solved on a local patch by preconditioned conjugate gradients using a geometric-multigrid V-cycle as the preconditioner. The background MPM discretization remains uniform: only the damage solve is localized. Two-way rigid-tool coupling converts MPM contact impulses into forces and torques on the tool, exposing material resistance directly to the policy. The resulting Gym-like simulator covers soft solids, brittle materials, granular media, and viscoplastic or semi-fluid media within a unified per-particle constitutive layer. We demonstrate cutting, scooping, and shoveling in six scenes, combining scripted tool motions with PPO policies trained on two cutting tasks.