Fluid-Structure Interaction problems are known to be very difficult to solve due to nonlinear and complex fluid-solid interactions. This complexity is exacerbated by having to simulate these interactions in complex geometries on small scales. However, using homogenization theory it is possible to upscale these complex fluid-solid interactions into effective equations. A classical example of this is supposing an infinitesimal pore-scale deformation, and yielding the classical Biot equations from rock microstructure physics. However, with nonlinear interfacial forces, and thus non-trivial pore-scale deformations, the resulting homogenization problems become highly nonlinear and yield, formally, a set of nonlinear Biot equations. This work aims to give better theoretical underpinnings to this idea by applying the homogenization technique of two-scale convergence to domains that have been deformed, e.g. in a previous time-step, and thus are non periodic. Utilizing a mapping technique, we obtain an augmented Stokes equation and two-scale homogenize them rigorously.
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