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.

翻译：精确处理含摩擦的接触问题仍然是物质点法（MPM）的核心瓶颈，涉及从可靠的接触点检测到摩擦接触定律（非穿透条件、库仑摩擦定律及最大耗散原理）的强制执行。本文提出了一种用于隐式MPM的摩擦接触处理流程，兼具精确性与鲁棒性。在碰撞检测阶段，我们采用以粒子为中心的几何图元进行接触点定位；在接触求解阶段，将摩擦接触问题构建为关于接触冲量的非线性互补问题（NCP），并采用交替方向乘子法（ADMM）进行求解。关键的是，该公式复用了隐式MPM的相同线性化过程，从而保证了计算效率与数值稳定性。该方法可无缝集成到隐式MPM计算循环中，且对材料本构模型、插值函数及传输方案等建模选择具有普适性。我们在七个代表性场景中对该方法进行了评估，涵盖弹性与弹塑性响应、简单与复杂的可变形几何结构，以及广泛的接触条件。总体而言，所提方法能够实现精确的接触定位、可靠的摩擦处理与广泛的通用性，为机器人及相关领域中基于MPM的仿真提供了实用解决方案。