Classical and sequential limit analysis revisited

Jean-Baptiste Leblond; Djimédo Kondo; Léo Morin; Almahdi Remmal

doi:10.1016/j.crme.2017.12.015

Classical and sequential limit analysis revisited

Jean-Baptiste Leblond ¹ ; Djimédo Kondo ¹ ; Léo Morin ² ; Almahdi Remmal ^1,³

¹ Sorbonne Universités, Université Pierre-et-Marie-Curie (UPMC), CNRS, UMR 7190, Institut Jean-Le Rond-d'Alembert, Tour 65-55, 4, place Jussieu, 75252 Paris cedex 05, France
² Arts et Métiers-ParisTech, CNAM, CNRS, UMR 8006, Laboratoire “Procédés et ingénierie en mécanique et matériaux”, 151, boulevard de l'Hôpital, 75013 Paris, France
³ AREVA, Tour Areva, 1, place Jean-Millier, 92084 Paris La Défense cedex, France

Comptes Rendus. Mécanique, Volume 346 (2018) no. 4, pp. 336-349.

Résumé

Classical limit analysis applies to ideal plastic materials, and within a linearized geometrical framework implying small displacements and strains. Sequential limit analysis was proposed as a heuristic extension to materials exhibiting strain hardening, and within a fully general geometrical framework involving large displacements and strains. The purpose of this paper is to study and clearly state the precise conditions permitting such an extension. This is done by comparing the evolution equations of the full elastic–plastic problem, the equations of classical limit analysis, and those of sequential limit analysis. The main conclusion is that, whereas classical limit analysis applies to materials exhibiting elasticity – in the absence of hardening and within a linearized geometrical framework –, sequential limit analysis, to be applicable, strictly prohibits the presence of elasticity – although it tolerates strain hardening and large displacements and strains. For a given mechanical situation, the relevance of sequential limit analysis therefore essentially depends upon the importance of the elastic–plastic coupling in the specific case considered.

Reçu le : 2017-12-13
Accepté le : 2017-12-14
Publié le : 2018-01-05

DOI : 10.1016/j.crme.2017.12.015

Mots clés : Classical limit analysis, Sequential limit analysis, Hill's approach, Drucker's approach, Elasticity, Strain hardening, Large displacements and strains

Affiliations des auteurs :

Jean-Baptiste Leblond ¹ ; Djimédo Kondo ¹ ; Léo Morin ² ; Almahdi Remmal ^{1, 3}

¹ Sorbonne Universités, Université Pierre-et-Marie-Curie (UPMC), CNRS, UMR 7190, Institut Jean-Le Rond-d'Alembert, Tour 65-55, 4, place Jussieu, 75252 Paris cedex 05, France
² Arts et Métiers-ParisTech, CNAM, CNRS, UMR 8006, Laboratoire “Procédés et ingénierie en mécanique et matériaux”, 151, boulevard de l'Hôpital, 75013 Paris, France
³ AREVA, Tour Areva, 1, place Jean-Millier, 92084 Paris La Défense cedex, France

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     author = {Jean-Baptiste Leblond and Djim\'edo Kondo and L\'eo Morin and Almahdi Remmal},
     title = {Classical and sequential limit analysis revisited},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {336--349},
     publisher = {Elsevier},
     volume = {346},
     number = {4},
     year = {2018},
     doi = {10.1016/j.crme.2017.12.015},
     language = {en},
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Jean-Baptiste Leblond; Djimédo Kondo; Léo Morin; Almahdi Remmal. Classical and sequential limit analysis revisited. Comptes Rendus. Mécanique, Volume 346 (2018) no. 4, pp. 336-349. doi : 10.1016/j.crme.2017.12.015. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.015/

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