[Minimiseurs de l'énergie explicits d'une barre incompressible, élastique, mais fragile, soumise à une extension uniaxiale]
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.
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@article{CRMATH_2010__348_17-18_1045_0,
author = {Mora-Corral, Carlos},
title = {Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension},
journal = {Comptes Rendus. Math\'ematique},
pages = {1045--1048},
publisher = {Elsevier},
volume = {348},
number = {17-18},
year = {2010},
doi = {10.1016/j.crma.2010.09.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.09.005/}
}
TY - JOUR AU - Mora-Corral, Carlos TI - Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension JO - Comptes Rendus. Mathématique PY - 2010 SP - 1045 EP - 1048 VL - 348 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.09.005/ DO - 10.1016/j.crma.2010.09.005 LA - en ID - CRMATH_2010__348_17-18_1045_0 ER -
%0 Journal Article %A Mora-Corral, Carlos %T Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension %J Comptes Rendus. Mathématique %D 2010 %P 1045-1048 %V 348 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.09.005/ %R 10.1016/j.crma.2010.09.005 %G en %F CRMATH_2010__348_17-18_1045_0
Mora-Corral, Carlos. Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 1045-1048. doi : 10.1016/j.crma.2010.09.005. http://www.numdam.org/articles/10.1016/j.crma.2010.09.005/
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