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In this paper we investigate the interaction of fluid flow with a thin porouselastic layer. We consider two fluid-filled bulk domains which are separated bya thin periodically perforated layer consisting of a fluid and an elastic solidpart. Thickness and periodicity of the layer are of order $\epsilon$, where$\epsilon$ is small compared to the size of the bulk domains. The fluid flow isdescribed by an instationary Stokes equation and the solid via linearelasticity. The main contribution of this paper is the rigorous homogenizationof the porous structure in the layer and the reduction of the layer to aninterface $\Sigma$ in the limit $\epsilon \to 0$ using two-scale convergence.The effective model consists of the Stokes equation coupled to a time dependentplate equation on the interface $\Sigma$ including homogenized elasticitycoefficients carrying information about the micro structure of the layer. Inthe zeroth order approximation we obtain continuity of the velocities at theinterface, where only a vertical movement occurs and the tangential componentsvanish. The tangential movement in the solid is of order $\epsilon$ and givenas a Kirchhoff-Love displacement. Additionally, we derive higher ordercorrectors for the fluid in the thin layer.

Derivation of Stokes-Plate-Equations modeling fluid flow interaction with thin porous elastic layers