Comptes Rendus
no. 11
Yield criteria for porous media in plane strain: second-order estimates versus numerical results
[Critère de plasticité des matériaux poreux en déformation plane : Estimations du second ordre et résultats numériques]
Joseph Pastor1 ; Pedro Ponte Castañeda2
1 Laboratoire matériaux composites, ESIGEC, Savoie Technolac, 73376 Le Bourget du Lac, France
2 Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA
Comptes Rendus. Mécanique, Volume 330 (2002) no. 11, pp. 741-747.

Cette Note présente une comparaison entre d'une part, les estimations issues d'une récente théorie d'homogénéisation, dite de « deuxième ordre », pour les matériaux parfaitement plastiques poreux en déformation plane, et d'autre part, les résultats homologues obtenus par analyse limite grâce une nouvelle technique de linéarisation du problème et une optimisation systématique des maillages éléments finis utilisés. Qualitativement parlant on observe un bon accord entre les deux approches sur la forme de la surface limite, avec mise en évidence d'un point anguleux sur l'axe hydrostatique, et sur la dépendance de la contrainte équivalente en cisaillement avec la porosité, contrainte dont la limite pour les faibles porosités apparaît non analytique. Ces deux caractéristiques ne sont pas prévues par le modèle de Gurson standard.

This Note presents a comparison of some recently developed “second-order” homogenization estimates for two-dimensional, ideally plastic porous media subjected to plane strain conditions with corresponding yield analysis results using a new linearization technique and systematically optimized finite elements meshes. Good qualitative agreement is found between the second-order theory and the yield analysis results for the shape of the yield surfaces, which exhibit a corner on the hydrostatic axis, as well as for the dependence of the effective flow stress in shear on the porosity, which is found to be non-analytic in the dilute limit. Both of these features are inconsistent with the predictions of the standard Gurson model.

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DOI : 10.1016/S1631-0721(02)01526-7
Keywords: porous media, homogenization, limit analysis, optimization
Mot clés : matériaux poreux, homogénéisation, analyse limite, optimisation
Joseph Pastor 1 ; Pedro Ponte Castañeda 2

1 Laboratoire matériaux composites, ESIGEC, Savoie Technolac, 73376 Le Bourget du Lac, France
2 Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104-6315, USA 
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Joseph Pastor; Pedro Ponte Castañeda. Yield criteria for porous media in plane strain: second-order estimates versus numerical results. Comptes Rendus. Mécanique, Volume 330 (2002) no. 11, pp. 741-747. doi : 10.1016/S1631-0721(02)01526-7. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01526-7/

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