Inserted: 13 feb 2003
Last Updated: 23 jan 2006
Journal: Ann. Inst. H. Poincaré Anal. Nonlin.
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