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In this paper, we derive an effective model for transport processes inperiodically perforated elastic media, taking into account, e.g., cyclicelastic deformations as they occur in lung tissue due to respiratory movement.The underlying microscopic problem couples the deformation of the domain with adiffusion process within a mixed \textit{Lagrangian}/\textit{Eulerian}formulation. After a transformation of the diffusion problem onto the fixeddomain, we use the formal method of two-scale asymptotic expansion to derivethe upscaled model, which is nonlinearly coupled through effectivecoefficients. The effective model is implemented and validated using anapplication-inspired model problem. Numerical solutions for both, cell problemsand macroscopic equations, are investigated and interpreted. We use simulationsto qualitatively determine the effect of the deformation on the transportprocess.

Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium