Comptes Rendus
A generalized continuum approach to describe instability pattern formation by a multiple scale analysis
[Une approche de milieu continu généralisé pour décrire des instabilités spatio-temporelles utilisant une analyse d'échelles multiples]
Comptes Rendus. Mécanique, Volume 334 (2006) no. 11, pp. 674-678.

L'évolution des instabilités spatio-temporelles peut se décrire macroscopiquement par des équations d'amplitude génériques de type Ginzburg–Landau. Dans l'exemple élémentaire du flambage d'une poutre, on établit une variante de cette approche, qui permet de prendre en compte des couplages entre instabilités locales et globales et qui traite de la même manière le champ moyen et la fluctuation. Le modèle final est un milieu continu généralisé, où les contraintes généralisées sont des coefficients de Fourier de la contrainte microscopique.

Macroscopic descriptions of instability pattern formation can be obtained by the generic amplitude equations of Ginzburg–Landau type. In the simple example of beam buckling, a variant of this approach is established, that permits one to account for the coupling between local and global instabilities. The mean field and the amplitude of the fluctuations are governed by similar equations. The resulting model is a generalized continuum, where the generalized stresses are Fourier coefficients of the microscopic stress.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2006.09.002
Keywords: Continuum mechanics, Ginzburg–Landau equation, Multiple scale, Local instability, Local–global coupling, Buckling
Mot clés : Milieux continus, Équation de Ginzburg–Landau, Échelles multiples, Instabilités locales, Couplage local–global, Flambage

Noureddine Damil 1 ; Michel Potier-Ferry 2

1 Laboratoire de calcul scientifique en mécanique, faculté des sciences Ben M'Sik, université Hassan II – Mohammedia, BP 7955, Sidi Othman, Casablanca, Morocco
2 Laboratoire de physique et mécanique des matériaux, UMR CNRS 7554, université Paul-Verlaine Metz, île du Saulcy, 57045 Metz, France
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Noureddine Damil; Michel Potier-Ferry. A generalized continuum approach to describe instability pattern formation by a multiple scale analysis. Comptes Rendus. Mécanique, Volume 334 (2006) no. 11, pp. 674-678. doi : 10.1016/j.crme.2006.09.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.09.002/

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