Calculus of Variations and Geometric Measure Theory

M. Friedrich - E. Mainini - P. Piovano - U. Stefanelli

Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule

created by mainini on 07 Jun 2017
modified on 19 Jul 2018


Published Paper

Inserted: 7 jun 2017
Last Updated: 19 jul 2018

Journal: Arch. Ration. Mech. Anal.
Year: 2018
Doi: 10.1007/s00205-018-1284-7


Carbon nanotubes are modeled as point configurations and investigated by minimizing configurational energies including two- and three-body interactions. Optimal configurations are identified with local minima and their fine geometry is fully characterized in terms of lower-dimensional problems. Under moderate tension, we prove the existence of periodic local minimizers, which indeed validates the so-called Cauchy–Born rule in this setting.