A stable and optimally convergent LaTIn‐CutFEM algorithm for multiple unilateral contact problems

Abstract

SummaryIn 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 2 bodies interacting at a single point.