Homogenization of a poroelasticity model for fiber-reinforced hydrogels

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, epsilon$$ \varepsilon $$, characterizing the heterogeneity of the medium. While doing epsilon -> 0$$ \varepsilon \to 0 $$, 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.