Dérivation rigoureuse de la théorie non linéaire des plaques et rigidité géométrique

Translated title of the contribution: Rigorous derivation of nonlinear plate theory and geometric rigidity

Gero Friesecke, Stefan Müller, Richard D. James

Research output: Contribution to journalArticlepeer-review

52 Scopus citations

Abstract

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 ν : (0, 1)3 → ℝ3. We show that the L2 distance of ∇ν from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations.

Translated title of the contributionRigorous derivation of nonlinear plate theory and geometric rigidity
Original languageFrench
Pages (from-to)173-178
Number of pages6
JournalComptes Rendus Mathematique
Volume334
Issue number2
DOIs
StatePublished - Jan 30 2002

Bibliographical note

Funding Information:
Acknowledgements. RDJ thanks AFOSR/MURI (F49620-98-1-0433), ARO (DAAG55-98-1-0335), NSF (DMS-0074043) and ONR (N00014-99-1-0925) for supporting his work. GF and SM were partially supported by the TMR network FMRX-CT98-0229.

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