  We present a new approach for the mechanically consistent modelling and
simulation of fluid-structure interactions with contact. The fundamental idea
consists of combining a relaxed contact formulation with the modelling of
seepage through a porous layer of co-dimension 1 during contact. For the
latter, a Darcy model is considered in a thin porous layer attached to a solid
boundary in the limit of infinitesimal thickness. In combination with a
relaxation of the contact conditions the computational model is both
mechanically consistent and simple to implement. We analyse the approach in
detailed numerical studies with both thick- and thin-walled solids, within a
fully Eulerian and an immersed approach for the fluid-structure interaction and
using fitted and unfitted finite element discretisations.
