A homogenization-based constitutive model for two-dimensional viscoplastic porous media

Kostas Danas; Martin I. Idiart; Pedro Ponte Castañeda

doi:10.1016/j.crme.2007.10.017

A homogenization-based constitutive model for two-dimensional viscoplastic porous media
[Un modèle d'homogénéisation pour les matériaux poreux viscoplastiques bi-dimensionnels]

Kostas Danas ^1,² ; Martin I. Idiart ^1,² ; Pedro Ponte Castañeda ^1,²

¹ Laboratoire de mécanique des solides, CNRS UMR7649, département de mécanique, École polytechnique, 91128 Palaiseau cedex, France
² Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA

Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 79-90.

Résumé
Abstract

On propose un modèle approximatif fondé sur la méthode d'homogénéisation non-linéaire dite du « second-ordre » pour estimer le comportement effectif des matériaux poreux viscoplastiques isotropes transverses. Le modèle est construit de manière à reproduire exactement le comportement hydrostatique des « assemblages de cylindres composites », c'est-à-dire la limite hydrostatique des matériaux poreux plastiques fournie par le critère de Gurson. Par conséquent, le nouveau modèle améliore les estimations de « second-ordre » existantes, qui se sont avérées excessivement raides aux triaxialités et aux non-linéarités suffisamment élevées. Le modèle proposé est comparé aux résultats exacts obtenus pour une classe particulière de matériaux poreux présentant des microstructures séquentiellement stratifiées. L'accord s'avère excellent pour la gamme entière des triaxialités, ainsi que pour toutes les valeurs de la porosité et de l'exposant caractérisant la non-linéarité du comportement.

An approximate model based on the so-called ‘second-order’ nonlinear homogenization method is proposed to estimate the effective behavior of viscoplastic porous materials exhibiting transversely isotropic symmetry. The model is constructed in such a way that it reproduces exactly the behavior of a ‘composite-cylinder assemblage’ in the limit of in-plane hydrostatic loading, and therefore coincides with the hydrostatic limit of Gurson's criterion for plastic porous materials. As a consequence, the new model improves on earlier ‘second-order’ homogenization estimates, which have been found to be overly stiff at sufficiently high triaxialities and nonlinearities. The proposed model is compared with exact results obtained for a special class of porous materials with sequentially laminated microstructures. The agreement is found to be excellent for the entire range of stress triaxialities, and all values of the porosity and nonlinearity considered.

Publié le : 2008-01-01

DOI : 10.1016/j.crme.2007.10.017

Keywords: Porous media, Homogenization, Nonlinear composites, Gurson criterion
Mot clés : Milieux poreux, Homogénéisation, Composites non-linéaires, Critère de Gurson

Affiliations des auteurs :

Kostas Danas ^{1, 2} ; Martin I. Idiart ^{1, 2} ; Pedro Ponte Castañeda ^{1, 2}

¹ Laboratoire de mécanique des solides, CNRS UMR7649, département de mécanique, École polytechnique, 91128 Palaiseau cedex, France
² Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA

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     title = {A homogenization-based constitutive model for two-dimensional viscoplastic porous media},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {79--90},
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     volume = {336},
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     doi = {10.1016/j.crme.2007.10.017},
     language = {en},
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Kostas Danas; Martin I. Idiart; Pedro Ponte Castañeda. A homogenization-based constitutive model for two-dimensional viscoplastic porous media. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 79-90. doi : 10.1016/j.crme.2007.10.017. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.017/

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