Title: A stable and optimally convergent LaTIn-Cut Finite Element Method for multiple unilateral contact problems,
Abstract: In this paper, we propose a novel unfitted finite element method for the
simulation of multiple body contact. The computational mesh is generated
independently of the geometry of the interacting solids, which can be
arbitrarily complex. The key novelty of the approach is the combination of
elements of the CutFEM technology, namely the enrichment of the solution field
via the definition of overlapping fictitious domains with a dedicated
penalty-type regularisation of discrete operators, and the LaTIn hybrid-mixed
formulation of complex interface conditions. Furthermore, the novel P1-P1
discretisation scheme that we propose for the unfitted LaTIn solver is shown to
be stable, robust and optimally convergent with mesh refinement. Finally, the
paper introduces a high-performance 3D level-set/CutFEM framework for the
versatile and robust solution of contact problems involving multiple bodies of
complex geometries, with more than two bodies interacting at a single point.