Publications
2002
Issue 33

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

33/2002

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

Gero Friesecke, Richard D. James and Stefan Müller

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 [G. Friesecke et al., C. R. Acad. Sci., Ser. I 334 (2002), 173--178] that for maps $v : (0, 1)^{3} \to R^{3}$ , the $L^{2}$ distance of $\nabla v$ from a single rotation is bounded by a multiple of the $L^{2}$ distance from the set $S O (3)$ of all rotations.

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Received:: 10.04.02

Published:: 10.04.02

MSC Codes:: 74K20, 73C50, 49J45

PACS:: 46.70.-p, 46.25.-y, 46.15.-x

Keywords:: plates, föppl von karman theory, gamma-convergence, nonlinear elasticity

Related publications

inJournal

2002 Repository Open Access

Gero Friesecke, Richard D. James and Stefan Müller

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

In: Comptes rendus mathematique, 335 (2002) 2, pp. 201-206

BibTex DOI: 10.1016/S1631-073X(02)02388-9