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A nonlinear model for inextensible rods as a low energy Gamma-limit of three-dimensional nonlinear elasticity
Maria Giovanna Mora and Stefan MüllerAbstract
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