Andy Wirtz and Alexander Popp

Within this work, we develop a combined contact and fluid-structure interaction (FSI) framework based on a monolithic coupling scheme. The aim is to achieve a smooth transition between FSI and frictional dry contact.

One of the major applications in biomechanics is the simulation of heart valves in a beating heart. Another example is the simulation of tires on a wet road in the field of automotive engineering.

For the contact discretization we use mortar finite element methods with finite deformations.

For FSI we employ a fixed-grid approach based on the extended finite element method (XFEM). Any moving-grid approach, e.g. arbitrary Lagrangean-Eulerian (ALE), would encounter serious problems in the case of approaching bodies, since fluid elements between contact interfaces would be completely squeezed together.

The main result of our work is the first finite element framework, which resolves the three major challenges of FSI simulations with contact. First, our approach enables an algorithmic handling of contact in an FSI simulation. Second, it incorporates a meaningful and stable fluid solution in small fluid gaps. And finally, it guarantees a smooth transition from FSI to frictional dry contact and vice versa.