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The Föppl-von Kármán plate theory as a low energy \(\Gamma\)-limit of nonlinear elasticity. (English. Abridged French version) Zbl 1041.74043
Summary: We show that the Föppl-von Kármán theory arises as a low energy \(\Gamma\)-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [the authors, ibid. 334, No. 2, 173–178 (2002; Zbl 1012.74043)] that for maps \(v:(0, 1)^3\to\mathbb{R}^3\), the \(L^2\) distance of \(\nabla v\) from a single rotation is bounded by a multiple of the \(L^2\) distance from the set SO(3) of all rotations.

MSC:
74K20 Plates
74B20 Nonlinear elasticity
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