[Une approche de milieu continu généralisé pour décrire des instabilités spatio-temporelles utilisant une analyse d'échelles multiples]
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.
Accepté le :
Publié le :
Mots-clés : Milieux continus, Équation de Ginzburg–Landau, Échelles multiples, Instabilités locales, Couplage local–global, Flambage
Noureddine Damil 1 ; Michel Potier-Ferry 2
@article{CRMECA_2006__334_11_674_0,
author = {Noureddine Damil and Michel Potier-Ferry},
title = {A generalized continuum approach to describe instability pattern formation by a multiple scale analysis},
journal = {Comptes Rendus. M\'ecanique},
pages = {674--678},
publisher = {Elsevier},
volume = {334},
number = {11},
year = {2006},
doi = {10.1016/j.crme.2006.09.002},
language = {en},
}
TY - JOUR AU - Noureddine Damil AU - Michel Potier-Ferry TI - A generalized continuum approach to describe instability pattern formation by a multiple scale analysis JO - Comptes Rendus. Mécanique PY - 2006 SP - 674 EP - 678 VL - 334 IS - 11 PB - Elsevier DO - 10.1016/j.crme.2006.09.002 LA - en ID - CRMECA_2006__334_11_674_0 ER -
%0 Journal Article %A Noureddine Damil %A Michel Potier-Ferry %T A generalized continuum approach to describe instability pattern formation by a multiple scale analysis %J Comptes Rendus. Mécanique %D 2006 %P 674-678 %V 334 %N 11 %I Elsevier %R 10.1016/j.crme.2006.09.002 %G en %F CRMECA_2006__334_11_674_0
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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