While numerical physical models of contact mechanics have become increasingly prevalent, the implementation of these models to efficiently resolve geometric contact with a robust contact search strategy remains lacking. Our research endeavors to address this gap by introducing a comprehensive solution with an exact geometric contact mechanics algorithm for thin shell finite elements with an explicit time scheme. The method has several key features, including precise geometrical resolution of self-contact interactions enabled by a sub-time-step marching method, adaptive data structures to minimize computational overhead, and a dedicated parallelization implementation with load-balancing capability. An efficient detection algorithm is implemented to reduce the natural polynomial time complexity of the problem by decomposing it into two phases: global and local phase contact detection. The impact equations are then applied to resolve the contact event by enforcing the conservation of kinematic energy and momentum. This contact algorithm is fully integrated with the MPI-based parallelization of the thin-shell finite element solver to ensure even load-balancing. The robustness and correctness of the algorithm is demonstrated in three numerical studies. Additionally, a strong scaling study showcases the scalability of the parallelization associated with the algorithm.

中文翻译：

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显式时间积分中薄壳有限元的并行几何接触算法


虽然接触力学的数值物理模型越来越普遍，但仍然缺乏这些模型通过强大的接触搜索策略有效解析几何接触的实现。我们的研究努力通过引入一种全面的解决方案来解决这一差距，该解决方案具有精确的几何接触力学算法，适用于具有显式时间方案的薄壳有限元。该方法具有几个关键功能，包括通过子时间步长行进方法实现的自接触交互的精确几何分辨率、可最大限度地减少计算开销的自适应数据结构，以及具有负载平衡功能的专用并行化实现。该算法实现了一种高效的检测算法，通过将问题分解为两个阶段来降低问题的自然多项式时间复杂度：全局相位和局部相位接触检测。然后，应用冲击方程通过强制执行运动能和动量守恒来求解接触事件。这种接触算法与基于 MPI 的薄壳有限元求解器并行化完全集成，以确保均匀的负载均衡。该算法的鲁棒性和正确性在三项数值研究中得到了证明。此外，一项强大的扩展研究展示了与算法相关的并行化的可扩展性。