The Föppl–von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity

Abstract

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. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 201–206.