Geodesic
The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity
[La théorie Föppl–von Kármán des plaques comme Γ-limite de l'élasticité non linéaire]
Friesecke, Gero1 ; James, Richard D.2 ; Müller, Stefan3
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
Comptes Rendus. Mathématique, Tome 335 (2002) no. 2, pp. 201-206

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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 v:(0,1) 3 →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 v:(0,1) 3 →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.

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

Friesecke, Gero 1 ; James, Richard D. 2 ; Müller, Stefan 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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     title = {The {F\"oppl{\textendash}von} {K\'arm\'an} plate theory as a low energy {\protect\emph{\ensuremath{\Gamma}}-limit} of nonlinear elasticity},
     journal = {Comptes Rendus. Math\'ematique},
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Friesecke, Gero; James, Richard D.; Müller, Stefan. The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity. Comptes Rendus. Mathématique, Tome 335 (2002) no. 2, pp. 201-206. doi: 10.1016/S1631-073X(02)02388-9

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