Comptes Rendus
no. 17-18
Mathematical Problems in Mechanics
Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension
[Minimiseurs de l'énergie explicits d'une barre incompressible, élastique, mais fragile, soumise à une extension uniaxiale]

Présenté par : John Ball

Carlos Mora-Corral1
1 BCAM – Basque Center for Applied Mathematics, Bizkaia Technology Park, building 500, 48160 Derio, Basque Country, Spain
Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 1045-1048.

Une barre rectangulaire faite d'un matériau incompressible, homogène, isotropique, hyper-élastique, mais fragile, est soumis à une extension uniaxiale. Nous prouvons que les minimiseurs de l'énergie correspondent, selon le coefficient de ténacité du matériau, soit à une déformation homogène, soit à une famille de déformations pour lesquelles une fracture horizontale casse le matériau en deux parties rectangulaires, chacune étant un mouvement rigide de la pièce non déformée.

A rectangular bar made of a hyperelastic, but brittle, incompressible homogeneous and isotropic material is subject to uniaxial extension. We prove that the energy minimizers are, depending on the toughness coefficient of the material, either the homogeneous deformation, or the family of deformations for which a horizontal fracture breaks the material in two rectangular pieces, each of which is a rigid motion of the undeformed piece.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.09.005
Carlos Mora-Corral 1

1 BCAM – Basque Center for Applied Mathematics, Bizkaia Technology Park, building 500, 48160 Derio, Basque Country, Spain 
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Carlos Mora-Corral. Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension. Comptes Rendus. Mathématique, Volume 348 (2010) no. 17-18, pp. 1045-1048. doi : 10.1016/j.crma.2010.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.09.005/

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