Contact phenomena are essential in understanding the behavior of mechanical systems. Existing computational approaches for simulating mechanical contact often encounter numerical issues, such as inaccurate physical predictions, energy conservation errors, and unwanted oscillations. We introduce an alternative technique, rooted in the non-overlapping Schwarz alternating method, originally developed for domain decomposition. In multi-body contact scenarios, this method treats each body as a separate, non-overlapping domain and prevents interpenetration using an alternating Dirichlet-Neumann iterative process. This approach has a strong theoretical foundation, eliminates the need for contact constraints, and offers flexibility, making it well-suited for multiscale and multi-physics applications. We conducted a numerical comparison between the Schwarz method and traditional methods like Lagrange multiplier and penalty methods, focusing on a benchmark impact problem. Our results indicate that the Schwarz alternating method surpasses traditional methods in several key areas: it provides more accurate predictions for various measurable quantities and demonstrates exceptional energy conservation capabilities. To address the issue of unwanted oscillations in contact velocities and forces, we explored various algorithms and stabilization techniques, ultimately opting for the naive-stabilized Newmark scheme for its simplicity and effectiveness. Furthermore, we validated the efficiency of the Schwarz method in a three-dimensional impact problem, highlighting its innate capacity to accommodate different mesh topologies, time integration schemes, and time steps for each interacting body.

翻译：接触现象是理解机械系统行为的关键。现有模拟机械接触的计算方法常面临数值问题，例如物理预测不准确、能量守恒误差以及非期望的振荡。我们引入一种替代技术，其根源在于最初为区域分解而发展的非重叠Schwarz交替法。在多体接触场景中，该方法将每个物体视为独立的非重叠区域，并通过交替的Dirichlet-Neumann迭代过程防止相互穿透。该方法具有坚实的理论基础，消除了接触约束的需求，并提供了灵活性，使其特别适用于多尺度与多物理场应用。我们针对一个基准冲击问题，将Schwarz法与传统方法（如拉格朗日乘子法和惩罚法）进行了数值比较。结果表明，Schwarz交替法在若干关键方面优于传统方法：它为各种可测量量提供了更精确的预测，并展现出卓越的能量守恒能力。为解决接触速度和力出现非期望振荡的问题，我们探讨了多种算法和稳定化技术，最终因其简洁性与有效性而选择了朴素稳定化的Newmark格式。此外，我们通过一个三维冲击问题验证了Schwarz法的效率，凸显了其在处理每个相互作用体时能自然适应不同网格拓扑、时间积分格式与时间步长的内在能力。