A parallel geometric contact algorithm for thin shell finite elements in explicit time integration

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.