A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity

Gero Friesecke, Richard D. James, Stefan Müller

Research output: Contribution to journalArticlepeer-review

472 Scopus citations

Abstract

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 rotations.

Original languageEnglish (US)
Pages (from-to)1461-1506
Number of pages46
JournalCommunications on Pure and Applied Mathematics
Volume55
Issue number11
DOIs
StatePublished - Nov 1 2002

Fingerprint Dive into the research topics of 'A Theorem on Geometric Rigidity and the Derivation of Nonlinear Plate Theory from Three-Dimensional Elasticity'. Together they form a unique fingerprint.

Cite this