An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material

Makrem Arfaoui; Khalil Mansouri; Ali Rezgui

doi:10.1016/j.crme.2008.07.003

An asymptotic finite plane deformation analysis of the elastostatic fields at a notch vertex of an incompressible hyperelastic material

Presented by: Huy Duong Bui

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

Comptes Rendus. Mécanique, Volume 336 (2008) no. 9, pp. 737-743.

Abstract
Résumé

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: 2008-04-10
Accepted: 2008-07-07
Published online: 2008-08-21

DOI: 10.1016/j.crme.2008.07.003

Keywords: Notch vertex, Hyperelasticity, Singularity, Asymptotic analysis, Mixed mode loading, Stress
Mots-clés : Coin d'un secteur, Hyperélasticité, Singularité, Analyse asymptotique, Chargement en mode mixte, Contrainte

Author's affiliations:

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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     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},
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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/

References
Cited by

[1] M.L. Williams Surface singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech. ASME, Volume 19 (1952), pp. 526-528

[2] P. Xiaolin On stress singularity at tips of plane notches, Mech. Res. Comm., Volume 13 (1986), pp. 173-178

[3] J.K. Knowles; E. Sternberg An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack, J. Elasticity, Volume 3 (1973), pp. 67-107

[4] J.K. Knowles; E. Sternberg Finite-deformation analysis of the elastostatic field near the tip of a crack: reconsideration and higher order results, J. Elasticity, Volume 4 (1974), pp. 201-233

[5] R.A. Stephenson The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials, J. Elasticity, Volume 12 (1982), pp. 65-99

[6] A.M. Tarantino The singular equilibrium field at the notch-tip of a compressible material in finite elastostatics, Z. Angew. Math. Phys., Volume 48 (1997), pp. 370-388

[7] A.M. Tarantino On extreme thinning at the notch tip of a neo-Hookean sheet, Quart J. Mech. Appl. Math., Volume 51 (1998)

[8] C.Q. Ru Finite deformations at the vertex of a bi-material wedge, Int. J. Fracture, Volume 84 (1997), pp. 325-350

[9] Y.C. Gao; T.S. Gao Notch-tip fields in rubber-like materials under tension and shear mixed load, Int. J. Fracture, Volume 78 (1996), pp. 283-298

[10] K. Mansouri, The singular equilibrium field at a notch vertex for finite plane strain of an incompressible Mooney–Rivlin hyperelastic material, Master thesis, Ecole Nationale d'Ingénieurs de Tunis, 2007

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