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Applied Micromechanics of Porous Materials by Jean-Louis Auriault (auth.), Luc Dormieux, Franz-Josef Ulm

By Jean-Louis Auriault (auth.), Luc Dormieux, Franz-Josef Ulm (eds.)

Poromechanics is the mechanics of porous fabrics and is now a good proven box in lots of engineering disciplines, starting from Civil Engineering, Geophysics, Petroleum Engineering to Bioengineering. despite the fact that, a rigorous process that hyperlinks the physics of the phenomena at stake in porous fabrics and the macroscopic behaviour continues to be lacking. This publication provides such an technique via homogenization concepts. carefully based in quite a few theories of micromechanics, those up scaling innovations are built for the homogenization of delivery houses, stiffness and power homes of porous materials.

The specified characteristic of this ebook is the stability among thought and alertness, supplying the reader with a finished creation to state of the art homogenization theories and functions to a wide range of actual existence porous fabrics: concrete, rocks, shales, bones, etc.

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Tensor D"*" is a Durely diffusive tensor: it is not modified by the advection. 4 Predominant Advection at Macroscale The observation time is now J. rpadv __ ^rpdif f and we have Vei = 1, Vi= e. 6) take the following form dc* DiJ^^^ Upscaling. =^ o^r. 36) 28 J. L. Auriault where c^^^ is a periodic function of y. 15) is still valid cC'^cfo'Cx,^). 39) where c^^^ is y-periodic. 39) over 1^* As expected the macroscopic behaviour shows only advection at the first order of approximation. 39). It is easily obtained %^ '^^dxj ^ dyj ^^ (^(o)_0-i<^(o)>^)^ ^' % inf)^.

0. 43) JQ% where the periodicity of rj* was used. The ellipticity property of tensor a yields the positivity of the left hand member of these equalities, that gives the result from the definition of /?. Particular cases. - Assume the material of the porous matrix is homogeneous. Tensor a* is now independent of y. 44) < eylmiC >-*kh ) > = {c^Jkh - ( ! - < / > ) O^ijkh) dijlm^ which yields < ^ M ^ > = ic^Jkh - (1 - <;Z^) — ^ij ~ ^khij ^khtf On an other hand, we have from the definition of a* e^/m(r7*) = (Q^*J - 0 / z j ) G^*j7m = ((^ " 0 ) ^ " ^khij dlhtt) ^Ijlm^ and /^* —< Vi,i >=" (1 ~ 4^)diiii - cl^ij dXhtt ^Ijii- In some applications, the material of the porous matrix is very slightly compressible.

Adler. Taylor dispersion in porous media: Analysis by multiple scale expansions. Advances in Water Resources, 18 (4):217-226, 1995. -L. Auriault and J. Lewandowska. On the validity of diff"usion/dispersion tests in soils. Engineering Transactions, 45 (3-4):395-417, 1997. -L. Auriault, C. Geindreau and P. Royer. Filtration law in rotating porous media. C. R. Acad. Sci. Paris, lib, 328:779-784, 2000. -L. Auriault, P. Royer and C. Geindreau. Filtration law for power-law fluids in anisotropic porous media.

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