提出一种高精度的摩擦接触求解方法，让材料点法模拟更真实可靠。
Frictional Contact Solving for Material Point Method
- 用粒子为中心的几何体精确定位接触点
- 将摩擦接触转为非线性互补问题，用ADMM求解
- 兼容多种材料模型，适合机器人仿真等应用
准确处理带摩擦的接触仍是材料点法（MPM）的核心挑战，涉及可靠的接触点检测和摩擦律的实现（不穿透、库仑摩擦及最大耗散原理）。本文提出一种用于隐式MPM的摩擦接触求解流程，兼具精度与鲁棒性。碰撞检测阶段，通过粒子为中心的几何体定位接触点；接触求解阶段，将摩擦接触建模为接触冲量上的非线性互补问题（NCP），并采用交替方向乘子法（ADMM）求解。关键在于该公式复用相同的隐式MPM线性化过程，保证了效率与数值稳定性。方法可无缝集成至隐式MPM循环中，且对材料定律、插值函数和传递方案等建模选择无依赖。在七个典型场景中进行评估，涵盖弹性与弹塑性响应、简单与复杂变形体，以及广泛接触条件。结果表明，该方法实现了精准的接触定位、可靠的摩擦处理和广泛的适用性，是机器人等领域基于MPM仿真的实用解决方案。
原文摘要 · Abstract (English)
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.
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