Comptes Rendus
On the control of crack growth in elastic media
[Sur le contrôle de la propagation de fissure en milieu élastique]
Comptes Rendus. Mécanique, Volume 336 (2008) no. 5, pp. 422-427.

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.

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.

Reçu le :
Accepté le :
Publié le :
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/

[1] M.C. Delfour; J.-P. Zolesio Shapes and Geometries – Analysis, Differential Calculus and Optimization, Advances in Design and Control, SIAM, 2001

[2] P. Destuynder An approach of the crack propagation control in structural dynamics, C. R. Acad. Sci. Paris, Sér. II, Volume 306 (1988), pp. 953-956

[3] P. Destuynder Remarks on a crack propagation control for stationary loaded structures, C. R. Acad. Sci. Paris, Sér. IIb, Volume 308 (1989)

[4] P. Destuynder Computation of an active control in fracture mechanics, Eur. J. Mech. A Solids, Volume 9 (1990)

[5] P. Destuynder; M. Djaoua; S. Lescure Quelques remarques sur la mécanique de la rupture élastique, J. Mec. Theor. Appl., Volume 2 (1983) no. 1, pp. 113-135

[6] A.A. Griffith The phenomena of rupture and flow in solids, Philos. Trans. Roy. Soc. London, Volume 46 (1920) no. 8, pp. 163-198

[7] P. Hild, A. Münch, Y. Ousset, On the active control of crack growth in elastic media, Preprint 38-2007, Univ. Franche-Comté

[8] A.-M. Khludnev; J. Sokolowski Modelling and control in solids mechanics, Inter. Series Numer., Volume 122 (1997), pp. 1-366

[9] J.-B. Leblond Mécanique de la rupture fragile et ductile, Hermes Sciences, 2003 (pp. 1–197)

[10] A. Münch; Y. Ousset Numerical simulation of delamination growth in curved interfaces, Comput. Methods Appl. Mech. Engrg., Volume 191 (2002), pp. 2045-2067

[11] A. Münch; P. Pedregal; F. Periago Optimal design of the damping set for the stabilization of the wave equation, J. Differential Equations, Volume 231 (2006), pp. 331-358

[12] M.T. Niane et al. Is it possible to cancel singularities in a domain with cracks?, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 115-188

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