Comptes Rendus
External estimate of the yield surface of an arbitrary ellipsoid containing a confocal void
Comptes Rendus. Mécanique, Volume 336 (2008) no. 11-12, pp. 813-819.

This work provides an external estimate, based on limit-analysis, of the yield surface of an arbitrary (non-spheroidal) ellipsoid made of ideal-plastic von Mises material and containing a confocal ellipsoidal void, under conditions of homogeneous boundary strain rate. The upper estimate of the overall plastic dissipation is based on consideration of incompressible velocity fields satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. One establishes the existence, uniqueness and explicit expression of such a velocity field for every overall strain rate tensor imposed on this boundary. The estimate of the overall plastic dissipation obtained may be used either as a rigorous upper bound, to assess the quality of existing models for the overall behavior of porous ductile materials containing ellipsoidal voids, or as an approximation helpful in the development of new such models.

On définit, par analyse-limite, une « estimation extérieure » de la surface de charge d'un ellipsoïde arbitraire (non axisymétrique) constitué d'un matériau parfaitement plastique de von Mises et contenant un vide ellipsoïdal confocal, sous des conditions de taux de déformation homogène au bord. L'estimation par excès de la dissipation plastique globale est fondée sur la considération de champs de vitesse incompressibles et satisfaisant des conditions de taux de déformation homogène sur tous les ellipsoïdes confocaux avec le vide et le bord extérieur. On établit l'existence, l'unicité et l'expression explicite d'un tel champ pour chaque tenseur de taux de déformation global imposé sur ce bord. L'estimation de la dissipation plastique globale obtenue peut être utilisée soit comme une majoration rigoureuse, pour évaluer la qualité de modèles existants du comportement global de matériaux poreux ductiles contenant des vides ellipsoïdaux, soit comme une approximation utile dans le développement de nouveaux modèles de ce genre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.10.006
Keywords: Limit-analysis, External approach, Hollow ellipsoid, Ductile materials, Void shape effects
Mot clés : Analyse-limite, Approche par l'extérieur, Ellipsoïde creux, Matériaux ductiles, Effets de forme des cavités

Jean-Baptiste Leblond 1; Mihai Gologanu 2

1 UPMC Université Paris 06, UMR 7190, Institut Jean-Le-Rond-d'Alembert, tour 65-55, 4, place Jussieu, 75005 Paris, France
2 Str. Simon Bolivar, Nr. 11, Sector 1, 011905 Bucharest, Romania
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Jean-Baptiste Leblond; Mihai Gologanu. External estimate of the yield surface of an arbitrary ellipsoid containing a confocal void. Comptes Rendus. Mécanique, Volume 336 (2008) no. 11-12, pp. 813-819. doi : 10.1016/j.crme.2008.10.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.10.006/

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