Calculus of Variations and Geometric Measure Theory

M. Cicalese - M. Ruf - F. Solombrino

On global and local minimizers of prestrained thin elastic rods

created by cicalese on 03 Jun 2016
modified by solombrin on 08 Oct 2017


Published Paper

Inserted: 3 jun 2016
Last Updated: 8 oct 2017

Journal: Calc. Var Pdes
Volume: 56
Number: 4
Pages: 115
Year: 2017
Doi: 10.1007/s00526-017-1197-6


We study the stable configurations of a thin $3$-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By $\Gamma$-convergence we derive a limit $1$-dimensional theory and show that isolated local minimizers of the limit model can be approached by local minimizers of the $3$-dimensional model. In the case of isotropic materials and for two-layers prestrained $3$-dimensional models the limit energy further simplifies to that of a Kirchhoff rod-model of an intrinsically curved beam. In this case we study the limit theory and study global and local stability of straight and helical configurations. Through some simple simulations we finally compare our results with real experiments.