Comptes Rendus
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.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.07.003
Keywords: Notch vertex, Hyperelasticity, Singularity, Asymptotic analysis, Mixed mode loading, Stress
Mot clés : Coin d'un secteur, Hyperélasticité, Singularité, Analyse asymptotique, Chargement en mode mixte, Contrainte

Makrem Arfaoui 1; Khalil Mansouri 1; Ali Rezgui 2

1 LGC, École nationale d'ingénieurs de Tunis (ENIT), BP 37 Le Belvédère, 1002 Tunis, Tunisia
2 MICHELIN, centre de Technologies Ladoux, 63040 Clermont-Ferrand cedex 09, France
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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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