Calculus of Variations and Geometric Measure Theory

L. Scardia

Asymptotic models for curved rods derived from nonlinear elasticity by $\Gamma$-convergence

created by scardia on 24 Jan 2007
modified on 01 Apr 2014


Published Paper

Inserted: 24 jan 2007
Last Updated: 1 apr 2014

Journal: Proc. Roy. Edinb. Soc. A
Year: 2007


We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity.

Keywords: dimension reduction, nonlinear elasticity, curved beams