An efficient and momentum conserving algorithm for enforcing contact between solid bodies is proposed. Previous advances in the material point method (MPM) led to a fast and simple, but potentially momentum violating, strategy for enforcing contact. This was achieved through a combination of velocity transfers between background and foreground grids, and a background grid velocity field update. We propose a modified strategy which ensures conservation of both linear and angular momentum with a novel use of the affine particle-in-cell (APIC) method. Two issues common to particle-in-cell based algorithms for contact are also addressed: material bodies tend to stick at a gap which is proportional to the grid spacing; and material points tend to stick together permanently when located within the same grid cell, making material rebound and friction challenging. We show that the use of APIC, combined with a grid transfer and momentum update algorithm results in contact being enforced at essentially zero gap. For the second issue, we propose a novel iterative scheme which allows particles interacting through the background grid to naturally separate after contact and enforce friction, while still satisfying momentum conservation.

中文翻译：

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基于仿射粒子网格传递的动量保持摩擦接触算法

提出了一种有效的动量守恒算法，用于加强实体之间的接触。物质点法 (MPM) 的先前进展导致了一种快速而简单但可能违反动量的策略来加强接触。这是通过背景和前景网格之间的速度传递以及背景网格速度场更新的组合来实现的。我们提出了一种改进的策略，该策略通过新颖的仿射粒子胞内 (APIC) 方法来确保线性和角动量的守恒。还解决了基于粒子内粒子接触算法的两个常见问题：材料体倾向于粘在与网格间距成正比的间隙处；当位于同一个网格单元内时，材料点往往会永久粘在一起，使材料回弹和摩擦具有挑战性。我们展示了 APIC 的使用，结合网格传输和动量更新算法，可以在基本零间隙下强制执行接触。对于第二个问题，我们提出了一种新颖的迭代方案，允许通过背景网格相互作用的粒子在接触后自然分离并强制摩擦，同时仍然满足动量守恒。