Calculus of Variations and Geometric Measure Theory

E. Mainini - H. Murakawa - P. Piovano - U. Stefanelli

Carbon-nanotube geometries: analytical and numerical results

created by mainini on 25 Jun 2016
modified on 27 Oct 2017


Published Paper

Inserted: 25 jun 2016
Last Updated: 27 oct 2017

Journal: Discrete Contin. Dyn. Syst.-Series S
Volume: 10
Number: 1
Year: 2017
Doi: 10.3934/dcdss.2017008


We investigate carbon-nanotubes under the perspective of geometry optimization. Nanotube geometries are assumed to correspond to atomic configurations which locally minimize Tersoff-type interaction energies. In the specific cases of so-called zigzag and armchair topologies, candidate optimal configurations are analytically identified and their local minimality is numerically checked. In particular, these optimal configurations do not correspond neither to the classical Rolled-up model nor to the more recent polyhedral model. Eventually, the elastic response of the structure under uniaxial testing is numerically investigated and the validity of the Cauchy-Born rule is confirmed.