Frictional Contact Solving for Material Point Method

TL;DR

The paper addresses the brittle handling of frictional contact in Material Point Method simulations by introducing a frictional-contact pipeline for implicit MPM. It localizes contact at sub-cell scales with particle-centric primitives and resolves friction by formulating a global nonlinear complementarity problem on the grid, solved with an ADMM scheme that reuses the implicit MPM admittance matrix. The method is agnostic to constitutive models, interpolation, and transfer schemes, and integrates naturally into the implicit MPM loop, enabling large time steps and robust multi-contact handling. Experiments across seven scenarios demonstrate precise contact localization, reliable friction enforcement, and broad applicability to elastic and elasto-plastic materials, with potential impact for robotics and related fields.

Abstract

Accurately handling contact with friction remains a core bottleneck for Material Point Method (MPM), from reliable contact point detection to enforcing frictional contact laws (non-penetration, Coulomb friction, and maximum dissipation principle). In this paper, we introduce a frictional-contact pipeline for implicit MPM that is both precise and robust. During the collision detection phase, contact points are localized with particle-centric geometric primitives; during the contact resolution phase, we cast frictional contact as a Nonlinear Complementarity Problem (NCP) over contact impulses and solve it with an Alternating Direction Method of Multipliers (ADMM) scheme. Crucially, the formulation reuses the same implicit MPM linearization, yielding efficiency and numerical stability. The method integrates seamlessly into the implicit MPM loop and is agnostic to modeling choices, including material laws, interpolation functions, and transfer schemes. We evaluate it across seven representative scenes that span elastic and elasto-plastic responses, simple and complex deformable geometries, and a wide range of contact conditions. Overall, the proposed method enables accurate contact localization, reliable frictional handling, and broad generality, making it a practical solution for MPM-based simulations in robotics and related domains.

Figures (3)

• Figure 1: Particle-centric contact detection and grid-based resolution. Left: A block is discretized into particles (red) and falls onto a planar surface meshed with tetrahedra (gray). Gray dots represent MPM grid nodes. Center: (broad phase) Overlaps between particle supports (green) and tetrahedral supports (black) on a shared grid yield candidate pairs. Particles selected for the narrow phase are shown in blue. Right: (narrow phase and solve) For each candidate (blue), the associated deformed tetrahedron (dark gray) is used to localize contact points and frames. Contacts are deposited onto the tetrahedra vertices and then transferred to grid nodes to assemble the contact Jacobian. The global frictional contact is written as an NCP and solved by ADMM. Grid velocities are corrected by the resulting contact impulses and mapped back to particles.
• Figure 2: Illustration of the seven experiments used in this paper: (1) a cube falling onto a plane; (2) multi-object interaction; (3) a cube sliding on an inclined plane; (4) a plastic cube sliding between two vertical planes; (5) a cube falling into a fluid-like medium; (6) a soft robotic finger rubbing against a plane; (7) a sphere impacting a quadrupod soft robot.
• Figure 3: Mean center-of-mass speed of the sliding cube along the plane direction as a function of the friction coefficient.