Nonlinear sequential laminates reproducing hollow sphere assemblages

Martín I. Idiart

doi:10.1016/j.crme.2007.04.003

Nonlinear sequential laminates reproducing hollow sphere assemblages
[Matériaux séquentiellement stratifiées non-linéaires reproduisant des ‘assemblages des sphères composites’]

Présenté par : André Zaoui

Martín I. Idiart ^1,²

¹ Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
² Laboratoire de mécanique des solides, CNRS UMR 7649, département de mécanique, École polytechnique, 91128 Palaiseau cedex, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 7, pp. 363-368.

Résumé
Abstract

On montre qu'une classe spéciale des matériaux poreux non-linéaires avec des microstructures ‘séquentiellement stratifiées’ isotropes reproduit exactement le comportement hydrostatique des ‘assemblage des sphères composites’ de Hashin. On argumente que ce résultat conforte la conjecture suivant laquelle le critère de Gurson pour les matériaux poreux plastiques, et son extension viscoplastique due à Leblond et al. (1994), peuvent constituer des bornes supérieures rigoureuses pour le seuil plastique hydrostatique des matériaux poreux contenant une distribution de porosité arbitraire mais macroscopiquement isotrope.

A special class of nonlinear porous materials with isotropic ‘sequentially laminated’ microstructures is found to reproduce exactly the hydrostatic behavior of ‘hollow sphere assemblages’. It is then argued that this result supports the conjecture that Gurson's approximate criterion for plastic porous materials, and its viscoplastic extension of Leblond et al. (1994), may actually yield rigorous upper bounds for the hydrostatic flow stress of porous materials containing an isotropic, but otherwise arbitrary, distribution of porosity.

Reçu le : 2007-02-05
Accepté le : 2007-04-03
Publié le : 2007-06-04

DOI : 10.1016/j.crme.2007.04.003

Keywords: Porous media, Homogenization, Nonlinear behavior
Mot clés : Milieux poreux, Homogénéisation, Comportement non linéaire

Affiliations des auteurs :

Martín I. Idiart ^{1, 2}

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     title = {Nonlinear sequential laminates reproducing hollow sphere assemblages},
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     pages = {363--368},
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     language = {en},
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Martín I. Idiart. Nonlinear sequential laminates reproducing hollow sphere assemblages. Comptes Rendus. Mécanique, Volume 335 (2007) no. 7, pp. 363-368. doi : 10.1016/j.crme.2007.04.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.04.003/

Bibliographie
Cité par

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[3] J.-L. Chaboche; P. Suquet; J. Beson Endommagement et changement d'échelle (M. Bornert; T. Bretheau; P. Gilormini, eds.), Homogénéisation en mécanique des matériaux, vol. 2, Hermes Science, 2001, pp. 91-146

[4] J.-P. Leblond, private communication (2006)

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[14] M.I. Idiart, Macroscopic behavior and field statistics in viscoplastic composites, Ph.D. Thesis, University of Pennsylvania, USA, 2006

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