[Analyse asymptotique en déformation finie plane des champs élastostatiques au coin d'un secteur pour un matériau hyperélastique incompressible]
Cette Note est consacrée à l'étude théorique des champs élastostatiques au coin d'un secteur soumis à des chargements généraux à l'infini. L'analyse est basée sur la théorie de l'hyperélasticité en déformation plane pour un matériau incompressible de Mooney–Rivlin. Nous approchons la solution en déplacement, près de la singularité, par un développement asymptotique mixte. La forme de la solution dépend de l'angle d'ouverture du coin et nous montrons qu'il y a singularité si le secteur est concave. Par ailleurs, nous montrons qu'un chargement en mode II pur donne lieu à l'ouverture du coin contrairement à l'élasticité linéaire.
This Note is devoted to the theoretical study of the elastostatic fields at a vertex notch under general far-field loading conditions. The analysis is based on the finite plane deformation hyperelasticity theory for an incompressible Mooney–Rivlin material. We approach the solution, near the singularity, by a mixed asymptotic development. We show that the shape of the solution depends on the opening angle of the notch and that there is singularity if the notch is concave. Furthermore, we show that a pure loading mode II gives rise to the opening of the notch vertex in contrast to the linear elasticity.
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Publié le :
Mot clés : Coin d'un secteur, Hyperélasticité, Singularité, Analyse asymptotique, Chargement en mode mixte, Contrainte
@article{CRMECA_2008__336_9_737_0,
author = {Makrem Arfaoui and Khalil Mansouri and Ali Rezgui},
title = {An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material},
journal = {Comptes Rendus. M\'ecanique},
pages = {737--743},
publisher = {Elsevier},
volume = {336},
number = {9},
year = {2008},
doi = {10.1016/j.crme.2008.07.003},
language = {en},
}
TY - JOUR AU - Makrem Arfaoui AU - Khalil Mansouri AU - Ali Rezgui TI - An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material JO - Comptes Rendus. Mécanique PY - 2008 SP - 737 EP - 743 VL - 336 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2008.07.003 LA - en ID - CRMECA_2008__336_9_737_0 ER -
%0 Journal Article %A Makrem Arfaoui %A Khalil Mansouri %A Ali Rezgui %T An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material %J Comptes Rendus. Mécanique %D 2008 %P 737-743 %V 336 %N 9 %I Elsevier %R 10.1016/j.crme.2008.07.003 %G en %F CRMECA_2008__336_9_737_0
Makrem Arfaoui; Khalil Mansouri; Ali Rezgui. An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material. Comptes Rendus. Mécanique, Volume 336 (2008) no. 9, pp. 737-743. doi : 10.1016/j.crme.2008.07.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.07.003/
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