Recent advances in the simulation of frictionally contacting elastodynamics with the Incremental Potential Contact (IPC) model have enabled inversion and intersection-free simulation via the application of mollified barriers, filtered line-search, and optimization-based solvers for time integration. In its current formulation the IPC model is constructed via a discrete constraint model, replacing non-interpenetration constraints with barrier potentials on an already spatially discretized domain. However, while effective, this purely discrete formulation prohibits convergence under refinement. To enable a convergent IPC model we reformulate IPC potentials in the continuous setting and provide a first, convergent discretization thereof. We demonstrate and analyze the convergence behavior of this new model and discretization on a range of elastostatic and dynamic contact problems, and evaluate its accuracy on both analytical benchmarks and application-driven examples.

翻译：近年来，基于增量势接触（IPC）模型的摩擦接触弹性动力学仿真取得了显著进展，通过应用平滑势垒函数、过滤线搜索以及基于优化的时间积分求解器，实现了无反转和无穿透的仿真。在当前公式中，IPC模型通过离散约束模型构建，用已在空间离散域上施加以势垒势能的形式替代了非穿透约束。然而，尽管有效，这种纯离散公式阻碍了网格细化下的收敛性。为了实现收敛的IPC模型，我们在连续域中重新构建了IPC势能，并首次提出了其收敛的离散化方案。我们在一系列弹性静力学和动力学接触问题上验证并分析了该新模型及离散化的收敛行为，并通过解析基准测试和应用驱动示例评估了其精度。