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In this paper, we propose a novel unfitted finite element method for thesimulation of multiple body contact. The computational mesh is generatedindependently of the geometry of the interacting solids, which can bearbitrarily complex. The key novelty of the approach is the combination ofelements of the CutFEM technology, namely the enrichment of the solution fieldvia the definition of overlapping fictitious domains with a dedicatedpenalty-type regularisation of discrete operators, and the LaTIn hybrid-mixedformulation of complex interface conditions. Furthermore, the novel P1-P1discretisation scheme that we propose for the unfitted LaTIn solver is shown tobe stable, robust and optimally convergent with mesh refinement. Finally, thepaper introduces a high-performance 3D level-set/CutFEM framework for theversatile and robust solution of contact problems involving multiple bodies ofcomplex geometries, with more than two bodies interacting at a single point.

A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems