Abstract
We consider a porous medium consisting of a deformable pore structure of the characteristic size ε. The solid skeleton is supposed to be elastic and the pores contain a viscous and incompressible fluid. Moreover, we consider that the solid part is connected but the fluid part is not connected. We analyse the case when the contrast of property number, and then the adimensional viscosity coefficients, are of order ε2. By homogenization we undertake a rigorous derivation of the diphasic effective behavior already observed in papers by M. Biot.
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Clopeau, T., Ferrín, J.L., Mikelic, A. (2002). Derivation of the Diphasic Biot’s Law for an Elastic Solid Matrix Containing Isolated Fluid Drops. In: Antonić, N., van Duijn, C.J., Jäger, W., Mikelić, A. (eds) Multiscale Problems in Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56200-6_5
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DOI: https://doi.org/10.1007/978-3-642-56200-6_5
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