The Incremental Potential Contact (IPC) method enables robust complex simulations of deformable objects with contact and friction. The key to IPC's robustness is its strict adherence to geometric constraints, avoiding intersections, which are a common cause of robustness issues in contact mechanics. A key element of the IPC approach to contact is a geometric barrier function, which is defined directly in the discrete setting. While IPC achieves its main goal of providing guarantees for contact constraints, its parameters need to be chosen carefully to avoid significant simulation artifacts and inaccuracies. We present a systematic derivation of an IPC-like continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence of shape, and absence of forces in rest configurations, based on the idea of candidate sets. Our potential is formulated in a way independent of surface discretization. This new potential is suitable for piecewise-linear surfaces and its efficiency is similar to standard IPC. We demonstrate its behavior and compare it to IPC on a range of challenging contact examples.

翻译：增量势能接触（IPC）方法能够实现对具有接触和摩擦的可变形物体进行鲁棒的复杂仿真。IPC的鲁棒性关键在于其严格遵守几何约束，避免穿透——这是接触力学中常见的鲁棒性问题根源。IPC接触方法的核心要素是几何势垒函数，该函数直接在离散框架中定义。尽管IPC实现了确保接触约束的主要目标，但其参数需谨慎选择以避免显著的仿真伪影和误差。本文基于候选集思想，从定义接触势能的自然需求集合（包括势垒特性、局域性、形状的可微依赖性以及无初始构型力）出发，系统推导了适用于光滑和分段光滑曲面的类IPC连续介质势能。该势能公式与表面离散化方式无关，适用于分段线性曲面，其效率与标准IPC相当。我们通过一系列具有挑战性的接触示例展示了该势能的行为，并与IPC进行了比较。