A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

@article{Friesecke2002ATO,
  title={A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity},
  author={Gero Friesecke and Richard D. James and Stefan M{\"u}ller},
  journal={Communications on Pure and Applied Mathematics},
  year={2002},
  volume={55}
}
The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐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 : U → ℝn, U ⊂ ℝn. We show that the L2‐distance of ∇v from a single rotation matrix is bounded by a multiple of the L2‐distance from the group SO(n) of all… 

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