Rigorous derivation of nonlinear plate theory and geometric rigidity

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 v:(0,1)3→R3. 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. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 173–178

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