Rigorous derivation of nonlinear plate theory and geometric rigidity
Gero Friesecke, Richard D. James, and Stefan Müller
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Submission date: 30. Aug. 2001
published in: Comptes rendus mathematique, 334 (2002) 2, p. 173-178
DOI number (of the published article): 10.1016/S1631-073X(02)02133-7
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We show that nonlinear plate theory arises as a -limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps . We show that the distance of from a single rotation is bounded by a multiple of the distance from the set SO(3) of all rotations.