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Jean-François Babadjian; Antonin Chambolle; Antoine Lemenant
Energy release rate for non-smooth cracks in planar elasticity
(Taux de restitution d’énergie pour des fissures non régulières en élasticité plane)
Journal de l'École polytechnique — Mathématiques, 2 (2015), p. 117-152, doi: 10.5802/jep.19
Article PDF | TeX source
Class. Math.: 74R10, 35J20, 49J45
Mots clés: Fissure, domaine non lisse, limite asymptotique, problème elliptique, ensemble singulier

Résumé - Abstract

Cet article est consacré à l’étude du taux de restitution d’énergie associé à une fissure fermée, connexe et de densité (de longueur) $1/2$ 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.

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