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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:
Feb 11, 2003
Published:
Feb 11, 2003
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