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.
Submitted November 29, 2012. Published April 05, 2013.
Math Subject Classifications: 35B27, 74Q05, 76M50.
Key Words: Poroelasticity equations; homogenization; two-scale convergence.
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| Abdelhamid Ainouz |
Laboratoire AMNEDP, Mathematics Department, USTHB
BP 32 ElAlia, Bab-Ezzouar, Algiers, Algeria
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