[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/
[1] Cellular Structures in Instabilities (J.E. Wesfreid; S. Zaleski, eds.), Lecture Notes in Physics, vol. 210, Springer-Verlag, Heidelberg, 1984
[2] Pattern formation out of equilibrium, Reviews of Modern Physics, Volume 65 (1993), pp. 851-1112
[3] Wavelength selection in the postbuckling of a long rectangular plate, International Journal of Solids and Structures, Volume 22 (1986), pp. 511-526
[4] Finite band width, finite amplitude convection, Journal of Fluid Mechanics, Volume 38 (1969), pp. 279-303
[5] Distant side walls cause slow amplitude modulation of cellular convection, Journal of Fluid Mechanics, Volume 38 (1969), pp. 203-224
[6] Theory of steady Ginzburg–Landau equation in hydrodynamic stability problems, European J. Mech. B/Fluids, Volume 8 (1989), pp. 229-268
[7] Cosserat overall modeling of heterogeneous materials, Mechanics Research Communications, Volume 25 (1998), pp. 449-454
[8] Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy, Computer Methods in Applied Mechanics and Engineering, Volume 193 (2004), pp. 5525-5550
[9] Stiffened plates and cylindrical shells under interactive buckling, Finite Elements in Analysis and Design, Volume 38 (2001), pp. 155-178
[10] Nonlinear interaction of geometrical and material properties in sandwich beam instabilities, International Journal of Solids and Structures, Volume 39 (2002), pp. 3717-3739
[11] Winkled membranes—Part 1: experiments, Journal of Mechanics of Materials and Structures, Volume 1 (2006), pp. 3-25
[12] Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, vol. 127, Springer-Verlag, Heidelberg, 1980
[13] Foundations of elastic postbuckling theory, Lecture Notes in Physics, vol. 288, Springer-Verlag, Heidelberg, 1987, pp. 1-82
Cité par Sources :
Commentaires - Politique