The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity
Gero Friesecke, Richard D. James, Stefan G. Müller · Comptes Rendus Mathématique · 2002
We show that the Föppl–von Kármán theory arises as a low energy Γ -limit of three-dimensional nonlinear elasticity. A key ingredient in the proof is a generalization to higher derivatives of our rigidity result [5] that for maps v : ( 0 , 1 ) 3 → ℝ 3 , 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.