Consistency of homogenization schemes in linear poroelasticity

Bernhard Pichler; Luc Dormieux

doi:10.1016/j.crme.2008.06.003

Consistency of homogenization schemes in linear poroelasticity

Presented by: André Zaoui

Bernhard Pichler ^1,² ; Luc Dormieux ²

¹ Vienna University of Technology (TU Wien), Institute for Mechanics of Materials and Structures, Karlsplatz 13/202, A-1040 Vienna, Austria
² LMSGC, Institut Navier, École nationale des ponts et chaussées, 6 et 8, avenue Blaise-Pascal, Champs-sur-Marne, 77455 Marne-la-Vallée, France

Comptes Rendus. Mécanique, Volume 336 (2008) no. 8, pp. 636-642.

Abstract
Résumé

In view of extending classical micromechanics of poroelasticity to the non-saturated regime, one has to deal with different pore stresses which may be affected by the size and the shape of the pores. Introducing the macrostrain and these pore stresses as loading parameters, the macrostress of a representative volume element of a porous material can be derived by means of Levin's theorem or by means of the direct formulation of the stress average rule, respectively. A consistency requirement for a given homogenization scheme is obtained from the condition that the two approaches should yield identical results. Classical approaches (Mori–Tanaka scheme, self-consistent scheme) are shown to be only conditionally consistent. In contrast, the Ponte Castañeda–Willis scheme proves to provide consistent descriptions both of porous matrix-inclusion composites and of porous polycrystals.

En vue d'étendre l'approche micromécanique de la poroélasticité dans le régime non saturé, il convient de prendre en compte différentes contraintes dans les pores, en fonction de leur forme et de leur taille. En adoptant la déformation macroscopique et ces contraintes de pores comme paramètres de chargement, la contrainte macroscopique peut être formulée à partir du théorème de Levin, ou bien en explicitant directement la règle de moyenne sur les contraintes. Une condition de cohérence du schéma d'homogénéisation retenu est obtenue en écrivant l'égalité des résultats de ces deux approches. On montre que les schémas classiques (Mori–Tanaka et autocohérent) ne satisfont cette condition que dans des cas particuliers. En revanche, elle est toujours vérifiée par le schéma de Ponte Castañeda et Willis.

Received: 2008-04-09
Accepted: 2008-06-09
Published online: 2008-07-30

DOI: 10.1016/j.crme.2008.06.003

Keywords: Porous media, Micromechanics, Levin's theorem, Mori–Tanaka scheme, Self-consistent scheme, Ponte Castañeda–Willis scheme
Mots-clés : Milieux poreux, Micromécanique, Théorème de Levin, Schéma de Mori–Tanaka, Schéma autocohérent, Schéma Ponte Castañeda–Willis

Author's affiliations:

Bernhard Pichler ^{1, 2}; Luc Dormieux ²

¹ Vienna University of Technology (TU Wien), Institute for Mechanics of Materials and Structures, Karlsplatz 13/202, A-1040 Vienna, Austria
² LMSGC, Institut Navier, École nationale des ponts et chaussées, 6 et 8, avenue Blaise-Pascal, Champs-sur-Marne, 77455 Marne-la-Vallée, France

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Bernhard Pichler; Luc Dormieux. Consistency of homogenization schemes in linear poroelasticity. Comptes Rendus. Mécanique, Volume 336 (2008) no. 8, pp. 636-642. doi : 10.1016/j.crme.2008.06.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.06.003/

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