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 demonstrated box in lots of engineering disciplines, starting from Civil Engineering, Geophysics, Petroleum Engineering to Bioengineering. despite the fact that, a rigorous method that hyperlinks the physics of the phenomena at stake in porous fabrics and the macroscopic behaviour continues to be lacking. This ebook provides such an method through homogenization suggestions. carefully based in quite a few theories of micromechanics, those up scaling innovations are constructed for the homogenization of delivery homes, stiffness and energy houses of porous materials.

The unique function of this e-book is the stability among idea and alertness, supplying the reader with a finished advent to cutting-edge homogenization theories and functions to a wide range of actual lifestyles porous fabrics: concrete, rocks, shales, bones, etc.

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H. Darcy. Les Fontaines Publiques de la Ville de Dijon, 1856. Dalmont, Paris. L Ene and E. Sanchez-Palencia. Equations et phenomene de surface pour I'ecoulement dans un modele de milieu poreux. Journal de Mecanique, 14 (1):73-108, 1975 (in French). M. -L. Guermond and P. Le Quere. Non linear corrections to Darcy's law at low Reynolds numbers. J. , 353:331-350, 1997. F. Gassmann. Uber die elastizitat poroser medien. Vierteljahrsschrift d. Naturf. Ges. Zilrich, 96:1-23, 1951 (in German). B. Keller.

Tensor c is an elastic tensor. Firstly, tensor c shows the symmetries of an elastic tensor. 14) where we put successively exij{u^^^) = SipSjq and ct = ^*''^ and e,,,(u(^)) = 5 , , V and a = The symmetries of the scalar product and tensor a* yield / a*^,, ey^jiCn eykkiCn dV* = - / f"'• a;^,, e , f c , ( r " ) dV* = - / K,,, eyUH^C^ dV* The last equality demonstrates the symmetry of c* (see the definition of c*). Secondly, tensor c* verifies an ellipticity condition as for a* ^l^jkh ^xij ^xkh > P ^xij exij, P > 0.

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)^. 43) Transport in Porous Media: Upscaling by Multiscale Asymptotic Expansions 29 where x*~^"^ is a periodic vector, of zero average which component x^^^ verifies ^Wjk + ^^—)^i = 0 on r*. 45) J It must be noticed that x*^^ ¥" X*^^ since now x*^^ depends on the velocity field and through it on the macroscopic gradient of pressure of components dp^^^/dxi.

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