Rigorous derivation of nonlinear plate theory and geometric rigidity
Gero Friesecke, Stefan G. Müller, Richard D. James · Comptes Rendus Mathématique · 2002
We show that nonlinear plate theory arises as a Γ -limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a sharp rigidity estimate for maps v : ( 0 , 1 ) 3 → ℝ 3 . We show that the L 2 distance of ∇ v from a single rotation is bounded by a multiple of the L 2 distance from the set SO(3) of all rotations.