Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.