Frictional Contact Solving for Material Point Method

TL;DR

This paper presents a robust and precise frictional contact solving pipeline for implicit Material Point Method (MPM), improving contact detection and friction law enforcement through a novel NCP formulation solved via ADMM, enhancing stability and efficiency.

Contribution

Introduces a frictional contact pipeline for implicit MPM that reuses the linearization, ensuring efficiency, stability, and broad applicability across various materials and geometries.

Findings

Accurate contact localization achieved across diverse scenes.

Reliable frictional handling demonstrated in complex scenarios.

Method integrates seamlessly with implicit MPM, improving robustness.

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.