Derivation of a Biot Plate System for a Thin Poroelastic Layer
Markus Gahn · SIAM Journal on Mathematical Analysis · 2025
Abstract. We study incompressible fluid flow through a thin poroelastic layer and rigorously derive a macroscopic model when the thickness of the layer tends to zero. Within the layer, we assume a periodic structure, and both the periodicity and the thickness of the layer are of order [Formula: see text], which is small compared to the length of the layer. The fluid flow is described by quasi-static Stokes equations, and for the elastic solid, we consider linear elasticity equations, and both are coupled via continuity of the velocities and the normal stresses. The aim is to pass to the limit [Formula: see text] in the weak microscopic formulation by using multiscale techniques adapted to the simultaneous homogenization and dimension reduction in continuum mechanics. The macroscopic limit model is given by a coupled Biot plate system consisting of a generalized Darcy law coupled to a Kirchhoff–Love-type plate equation including the Darcy pressure.