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            <funder>MF and FG were partially supported by the French National Research Agency (ANR), trough the SIMR project (ANR-19-CE45-0020). EB was partially supported by the EPSRC grants EP/P01576X/1 and EP/T033126/1. EB, MF and FG also acknowledge support by Inria through the Associated Team IMFIBIO.</funder>
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                <term xml:lang="en">Fluid-structure interaction</term>
                <term xml:lang="en">Contact mechanics</term>
                <term xml:lang="en">Nitsche's method</term>
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              <p>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.</p>
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