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MiS Preprint
33/2002
The Föppl-von Kármán plate theory as a low energy Gamma limit of nonlinear elasticity
Gero Friesecke, Richard D. James and Stefan Müller
Abstract
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 [G. Friesecke et al., C. R. Acad. Sci., Ser. I 334 (2002), 173--178] that for maps $v:(0,1)^3 \rightarrow \mathbb{R}^3$, 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.
