A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity
by
Gero Friesecke, Richard D. James and Stefan Muller
in
Comm. Pure and Appl. Math., LV, 1461–1506., 2002.
Category: Journal Article
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Abstract:
The energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a 0-limit of three-dimensional nonlinear elasticity theory as the thickness of a plate goes to zero. A key ingredient in the proof is a sharp rigidity estimate for maps v V U ! Rn, U Rn. We show that the L2-distance of rv from a single rotation matrix is bounded by a multiple of the L2-distance from the group SO.n/ of all rotations.
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