The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity
Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 201-206.

We show that the Föppl–von Kármán theory arises as a low energy Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [5] that for maps $\mathrm{v}:{\left(0,1\right)}^{3}\to {ℝ}^{3}$, the L2 distance of ∇v from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.

Nous montrons que la théorie Föppl–von Kármán des plaques émerge comme Γ-limite de la théorie de l'élasticité tridimensionnelle. La démonstration repose sur une generalisation aux derivées d'ordre supérieur de notre résultat de rigidité [5] que pour des fonctions $\mathrm{v}\phantom{\rule{0.277778em}{0ex}}:{\left(0,1\right)}^{3}\to {ℝ}^{3}$, la distance L2 de ∇v à une rotation est bornée par un multiple de la distance L2 à l'ensemble SO(3) des rotations.

Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02388-9

Gero Friesecke 1; Richard D. James 2; Stefan Müller 3

1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
2 Department of Aerospace Engineering and Mechanics, 107 Akerman Hall, University of Minnesota, Minneapolis, MN 55455, USA
3 Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22-26, 04103 Leipzig, Germany
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Gero Friesecke; Richard D. James; Stefan Müller. The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity. Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 201-206. doi : 10.1016/S1631-073X(02)02388-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02388-9/

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