摩擦接触求解用于材料点法
Frictional Contact Solving for Material Point Method
AI总结：
本文提出一种适用于隐式MPM的摩擦接触求解方法，通过非线性互补问题和ADMM方案实现精确且稳健的摩擦接触处理，适用于多种变形几何和接触条件。
摘要：
准确处理摩擦接触仍然是材料点法（MPM）的核心瓶颈，从可靠的接触点检测到执行摩擦接触定律（非穿透、库仑摩擦和最大耗散原理）。在本文中，我们介绍了一种适用于隐式MPM的摩擦接触流程，该流程既精确又稳健。在碰撞检测阶段，通过粒子中心的几何原语定位接触点；在接触解决阶段，我们将摩擦接触转化为非线性互补问题（NCP）在接触冲量上，并使用交替方向乘子法（ADMM）方案求解。关键的是，该公式重用了相同的隐式MPM线性化，从而获得效率和数值稳定性。该方法无缝集成到隐式MPM循环中，并对建模选择无感，包括材料定律、插值函数和传输方案。我们评估了其在七个具有代表性的场景中的表现，涵盖了弹性与弹塑性响应、简单与复杂变形几何体以及广泛的接触条件。总体而言，所提出的方法实现了准确的接触定位、可靠的摩擦处理和广泛的通用性，使其成为MPM基于模拟在机器人及相关领域中的实用解决方案。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
