We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two‐phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a priori known interface movement because of phase transformations. After transforming the moving geometry to an ϵ‐periodic, fixed reference domain, we establish the well‐posedness of the model and derive a number of ϵ‐independent a priori estimates. Via a two‐scale convergence argument, we then show that the ϵ‐dependent solutions converge to solutions of a corresponding upscaled model with distributed time‐dependent microstructures. Copyright © 2017 John Wiley & Sons, Ltd.

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In this paper, the analysis and homogenization of a poroelastic model for the hydro-mechanical response of fiber-reinforced hydrogels are considered.Here, the medium in question is considered to be a highly heterogeneous two-component media composed of a connected fiber-scaffold with periodically distributed inclusions of hydrogel. While the fibers are assumed to be elastic, the hydromechanical response of hydrogel is modeled via Biot's poroelasticity.We show that the resulting mathematical problem admits a unique weak solution and investigate the limit behavior (in the sense of two-scale convergence) of the solutions with respect to a scale parameter, 𝜀, characterizing the heterogeneity of the medium. While doing 𝜀 → 0, we arrive at an effective model where the micro variations of the pore pressure give rise to a micro stress correction at the macro scale.

We report on a reaction-diffusion model posed on multiple spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles. The model is able to account for the heterogeneity of the internal porous structure of the layer. For simplicity, we represent the microstructures as discs with prescribed initial random distribution of radii. As microstructures grow due to the deposition of populations of colloidal particles, local clogging becomes possible, that is neighbouring disks may touch each other. We investigate how distributions of evolving microstructures influence the transport and storage properties of porous layers. As working tool, we propose a FD-FEM discretization of the multiscale model. We illustrate numerically local clogging effects on the dispersion tensor and quantify herewith the layer’s performance with respect to both the efficiency of the transport and the storage capacity. The presented model and numerical approach can be extended in a rather straightforward way to handle slightly more complex geometrical settings like thin porous structures with multi-layers in 2D, or single layers in 3D.