An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields

Vincent Monchiet; Eric Charkaluk; Djimedo Kondo

doi:10.1016/j.crme.2006.12.002

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
[Une amélioration des modèles de type Gurson pour les mileux poreux par utilisation des champs tests d'Eshelby]

Présenté par : Pierre Suquet

Vincent Monchiet ¹ ; Eric Charkaluk ¹ ; Djimedo Kondo ¹

¹ Laboratoire de mécanique de Lille-UMR CNRS 8107, université de sciences et technologies de Lille, cité scientifique, 59655 Villeneuve d'Ascq cedex, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 32-41.

Résumé
Abstract

On présente de nouvelles expressions du critère macroscopique de milieux poreux constitués d'une matrice rigide parfaitement plastique contenant des cavités allongées ou aplaties. L'approche proposée, formulée dans le cadre de l'analyse limite, repose sur la considération de champs test de vitesse de type Eshelby pour la détermination de la dissipation macroscopique. On démontre que les résultats obtenus améliorent de manière significative les critères de milieux poreux ductiles existants. De plus, pour les faibles triaxialités de contrainte, ces nouveaux résultats s'accordent aussi parfaitement avec les bornes (non linéaires) d'Hashin–Shtrikhman établies par Ponte-Castañeda et par Suquet.

New expressions of the macroscopic criteria of perfectly plastic rigid matrix containing prolate and oblate cavities are presented. The proposed approach, derived in the framework of limit analysis, consists in the consideration of Eshelby-like trial velocity fields for the determination of the macroscopic dissipation. It is shown that the obtained results significantly improve existing criteria for ductile porous media. Moreover, for low stress triaxialities, these new results also agree perfectly with the (nonlinear) Hashin–Shtrikhman bound established by Ponte-Castañeda and Suquet.

Reçu le : 2006-07-11
Accepté le : 2006-10-27
Publié le : 2007-01-01

DOI : 10.1016/j.crme.2006.12.002

Keywords: Computational solid mechanics, Ductile porous metals, Generalized Gurson criterion, Prolate and oblate voids, Eshelby velocity fields, Limit analysis
Mot clés : Mécanique des solides numériques, Métaux ductiles poreux, Critère de Gurson généralisé, Cavités allongées et aplaties, Champ de vitesse d'Eshelby, Analyse limite

Affiliations des auteurs :

Vincent Monchiet ¹ ; Eric Charkaluk ¹ ; Djimedo Kondo ¹

¹ Laboratoire de mécanique de Lille-UMR CNRS 8107, université de sciences et technologies de Lille, cité scientifique, 59655 Villeneuve d'Ascq cedex, France

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     author = {Vincent Monchiet and Eric Charkaluk and Djimedo Kondo},
     title = {An improvement of {Gurson-type} models of porous materials by using {Eshelby-like} trial velocity fields},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {32--41},
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     doi = {10.1016/j.crme.2006.12.002},
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Vincent Monchiet; Eric Charkaluk; Djimedo Kondo. An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields. Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 32-41. doi : 10.1016/j.crme.2006.12.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.12.002/

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