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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.
Reviewer: Jan Franců (Brno)

##### MSC:
 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
##### Keywords:
homogenization; poro-elasticity; two-scale convergence
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