Cet article est consacré à l’étude du taux de restitution d’énergie associé à une fissure fermée, connexe et de densité (de longueur) en pointe de fissure, sans autre hypothèse de régularité. Tout d’abord, la limite de blow-up du déplacement à la pointe est analysée, ainsi que la convergence vers une certaine fonction, positivement 1/2-homogène, explicite. Le taux de restitution d’énergie, qui est la dérivée de l’énergie élastique par rapport à un incrément infinitésimal de fissure, est alors obtenu comme solution d’un problème variationnel.
This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with (length) density at the tip, without further regularity assumptions. First, the blow-up limit of the displacement is analyzed, and the convergence to a (known) positively -homogenous function in the cracked plane is established. Then, the energy release rate, which is the derivative of the elastic energy with respect to an infinitesimal additional crack increment, is obtained as the solution of a variational problem.
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@article{JEP_2015__2__117_0,
author = {Jean-Fran\c{c}ois Babadjian and Antonin Chambolle and Antoine Lemenant},
title = {Energy release rate for non-smooth cracks in~planar elasticity},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {117--152},
publisher = {\'Ecole polytechnique},
volume = {2},
year = {2015},
doi = {10.5802/jep.19},
mrnumber = {3366673},
zbl = {1325.74126},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.19/}
}
TY - JOUR AU - Jean-François Babadjian AU - Antonin Chambolle AU - Antoine Lemenant TI - Energy release rate for non-smooth cracks in planar elasticity JO - Journal de l’École polytechnique — Mathématiques PY - 2015 SP - 117 EP - 152 VL - 2 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.19/ DO - 10.5802/jep.19 LA - en ID - JEP_2015__2__117_0 ER -
%0 Journal Article %A Jean-François Babadjian %A Antonin Chambolle %A Antoine Lemenant %T Energy release rate for non-smooth cracks in planar elasticity %J Journal de l’École polytechnique — Mathématiques %D 2015 %P 117-152 %V 2 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.19/ %R 10.5802/jep.19 %G en %F JEP_2015__2__117_0
Jean-François Babadjian; Antonin Chambolle; Antoine Lemenant. Energy release rate for non-smooth cracks in planar elasticity. Journal de l’École polytechnique — Mathématiques, Tome 2 (2015), pp. 117-152. doi : 10.5802/jep.19. https://jep.centre-mersenne.org/articles/10.5802/jep.19/
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