Rigorous derivation of nonlinear plate theory and geometric rigidity
Comptes Rendus. Mathématique, Volume 334 (2002) no. 2, pp. 173-178.

We show that nonlinear plate theory arises as a Γ-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps $\mathrm{v}:{\left(0,1\right)}^{3}\to {ℝ}^{3}$. We show that 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 non linéaire des plaques émerge comme Γ-limite de la théorie de l'élasticité tridimensionnelle. La démonstration repose sur un résultat de rigidité pour des fonctions $\mathrm{v}\phantom{\rule{0.277778em}{0ex}}:{\left(0,1\right)}^{3}\to {ℝ}^{3}$. Nous montrons que la distance L2 de ∇v d'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)02133-7

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

1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
2 Max-Planck Institute for Mathematics in the Sciences, Inselstr. 22–26, 04103 Leipzig, Germany
3 Department of Aerospace Engineering and Mechanics, 107 Akerman Hall, University of Minnesota, Minneapolis, MN 55455, USA
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Gero Friesecke; Stefan Müller; Richard D. James. Rigorous derivation of nonlinear plate theory and geometric rigidity. Comptes Rendus. Mathématique, Volume 334 (2002) no. 2, pp. 173-178. doi : 10.1016/S1631-073X(02)02133-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02133-7/

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