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From mixture theory to Biot’s approach for porous media. (English) Zbl 0932.74014
Summary: Two apparently different approaches are used in dealing with the mechanics of a deformable porous medium: mixture theories on the one hand, and purely macroscale theories, which are mainly associated with the work of Biot, on the other hand. In the mixture theories, the porous medium is represented by spatially superposed interacting media, while macroscale theories assume that standard concepts of continuum mechanics are still relevant at the macro-level. The aim of this paper is two-fold. First, we show that the macroscale field equations derived from mixture theories can be reformulated in terms of the measurable quantities involved in the macroscale theories. Second, we demonstrate how these field equations, including the fundamental inequality obtained from the second law, entail the existence of a macroscale \(\Psi\)-potential, upon which a thermo-dynamically consistent formulation of the constitutive equations can be firmly founded.
Reviewer: Reviewer (Berlin)

MSC:
74E05 Inhomogeneity in solid mechanics
74A15 Thermodynamics in solid mechanics
76S05 Flows in porous media; filtration; seepage
80A17 Thermodynamics of continua
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