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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 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
13/2003

A nonlinear model for inextensible rods as a low energy Gamma-limit of three-dimensional nonlinear elasticity

Maria Giovanna Mora and Stefan Müller

Abstract

Using a variational approach we rigorously deduce a nonlinear model for inextensible rods from three-dimensional nonlinear elasticity, passing to the limit as the diameter of the rod goes to zero. The theory obtained is analogous to the Föppl-von Káe;rmán theory for plates. We also derive an asymptotic expansion of the solution and compare it to a similar expansion which Murat and Sili obtained starting from three-dimensional linear elasticity.

Received:
11.02.03
Published:
11.02.03
MSC Codes:
74K10, 49J45
Keywords:
nonlinear elasticity, rod theory, gamma-convergence

Related publications

inJournal
2004 Repository Open Access
Maria Giovanna Mora and Stefan Müller

A nonlinear model for inextensible rods as a low energy Gamma-limit of three-dimensional nonlinear elasticity

In: Annales de l'Institut Henri Poincaré / C, 21 (2004) 3, pp. 271-293