Comptes Rendus
On the control of crack growth in elastic media
Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 422-427.

In the framework of linear fracture theory, the Griffith criterion postulates the growth of any crack if the corresponding so-called energy release rate, defined as the variation of the mechanical energy, reaches a critical value. We consider in this Note the optimal location problem which consists in minimizing this rate by applying to the structure an additional boundary load having a support which is disjoint from the support of the initial load possibly responsible of the growth. We give a sufficient well-posedness condition, introduce a relaxed problem in the general case, and then present a numerical experiment which suggests that the original nonlinear problem is actually well-posed.

Dans le cadre de la mécanique linéaire de la rupture, le critère de Griffith postule la croissance d'une fissure si le taux de restitution de l'énergie associé excède une valeur critique. On considère dans cette Note le problème d'optimisation de position qui consiste à minimiser ce taux en appliquant à la structure un chargement de frontière additionnel de support disjoint du chargement initial. On donne une condition suffisante d'existence de solution, on introduit une relaxation du problème dans le cas général, puis on présente une simulation numérique suggérant que ce problème non linéaire est en fait bien posé.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.02.005
Keywords: Solids and structures, Linear fracture mechanics, Control
Mot clés : Solides et structures, Mécanique linéaire de la rupture, Contrôle

Patrick Hild 1; Arnaud Münch 1; Yves Ousset 2

1 Laboratoire de mathématiques, université de Franche-Comté, UMR CNRS 6623, 25030 Besançon, France
2 ONERA, DMSE, 29, avenue de la division Leclerc, BP 72, 92322 Châtillon cedex, France
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Patrick Hild; Arnaud Münch; Yves Ousset. On the control of crack growth in elastic media. Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 422-427. doi : 10.1016/j.crme.2008.02.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.02.005/

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