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MiS Preprint
58/2001
Rigorous derivation of nonlinear plate theory and geometric rigidity
Gero Friesecke, Richard D. James and Stefan Müller
Abstract
We show that nonlinear plate theory arises as a $\Gamma$-limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps $v:(0,1)^3 \to \mathbb{R}^3$. We show that 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.
