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

Maria Giovanna Mora and Stefan Müller

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Submission date: 11. Feb. 2003
Pages: 31
published in: Annales de l'Institut Henri Poincaré / C, 21 (2004) 3, p. 271-293 
DOI number (of the published article): 10.1016/j.anihpc.2003.08.001
Bibtex
MSC-Numbers: 74K10, 49J45
Keywords and phrases: nonlinear elasticity, rod theory, gamma-convergence
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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 Kármán 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.