Calculus of Variations and Geometric Measure Theory

M. G. Mora - S. Müller

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

created on 13 Feb 2003
modified by mora on 23 Jan 2006


Published Paper

Inserted: 13 feb 2003
Last Updated: 23 jan 2006

Journal: Ann. Inst. H. Poincaré Anal. Nonlin.
Volume: 21
Pages: 271-293
Year: 2004


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.

Keywords: Gamma-convergence, nonlinear elasticity, rod theory