Frictional Contact Solving for Material Point Method

2026-02-02

AI Summary

This work addresses the limited accuracy and robustness in modeling frictional contact within the Material Point Method (MPM) by proposing a unified solver framework for implicit MPM. The approach precisely locates contact points using particle-centered geometric primitives and formulates frictional contact—including impenetrability, Coulomb friction, and the principle of maximum dissipation—as a nonlinear complementarity problem (NCP) in terms of contact impulses. An ADMM-based algorithm is employed for efficient solution. Notably, this is the first method to cast frictional contact uniformly as an NCP and embed it within implicit MPM while reusing its linearized structure. The framework demonstrates high-precision contact localization, reliable friction handling, and broad applicability across seven diverse scenarios involving elastic and elastoplastic materials, complex geometries, and varied contact conditions.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Intelligent Robots: Motion and Path Planning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Algorithmic accountability and transparency on the web

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.

Problem

• frictional contact
• Material Point Method
• contact detection
• Coulomb friction
• non-penetration

Innovation

• Material Point Method
• Frictional Contact
• Nonlinear Complementarity Problem
• ADMM
• Implicit MPM