zbMATH — the first resource for mathematics

Homogenized double porosity models for poro-elastic media with interfacial flow barrier. (English) Zbl 1249.35016
In the paper a Barenblatt-Biot consolidation model for flows in porous elastic media is derived by homogenization. The starting Biot micro model assumes a two-component material in a domain \(\Omega \) with inclusions \(\Omega _\varepsilon ^{(2)}\) \(\varepsilon \)-periodically distributed in the matrix \(\Omega _\varepsilon ^{(1)}\). Both volumes are assumed to be saturated with a slightly compressible viscous fluid. All the coefficients of the constitutive relations are assumed to be \(\varepsilon \)-periodic. The system consists of the vector equilibria equation for displacement coupled with the scalar evolution equation for pressure on both \((0,T)\times \Omega _\varepsilon ^{(i)}\). The system is completed with Deresiewicz-Skalak condition on the \(\varepsilon \)-periodic interface of the components. Using the two-scale convergence technique homogenization of this micro model leads to the Aifantis double porosity model on \((0,T)\times \Omega \). Comparison and remarks on various models are included.

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
74Q05 Homogenization in equilibrium problems of solid mechanics
76M50 Homogenization applied to problems in fluid mechanics
Full Text: EuDML Link