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Homogenization of a double porosity model in deformable media. (English) Zbl 1288.35038
Summary: The article addresses the homogenization of a family of micro-models for the flow of a slightly compressible fluid in a poroelastic matrix containing periodically distributed poroelastic inclusions, with low permeabilities and with imperfect contact on the interface. The micro-models are based on Biot’s system for consolidation processes in each phase, with interfacial barrier formulation. Using the two-scale convergence technique, it is shown that the derived system is a general model of that proposed by Aifantis, plus an extra memory term.

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
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