Calculus of Variations and Geometric Measure Theory

M. Friedrich - E. Mainini - P. Piovano

Atomistic potentials and the Cauchy-Born rule for carbon nanotubes: a review

created by mainini on 27 Sep 2019
modified on 28 Dec 2020


Published Paper

Inserted: 27 sep 2019
Last Updated: 28 dec 2020

Journal: Rendiconti Sem. Mat. Univ. Pol. Torino
Volume: 77
Number: 2
Pages: 79-98
Year: 2019

ArXiv: 1909.12023 PDF


Carbon nanotubes are modeled as point particle configurations in the framework of Molecular Mechanics, where interactions are described by means of short range attractive-repulsive potentials. The identification of local energy minimizers yields a variational description for the stability of rolled-up hexagonal-lattice structures. Optimality of periodic configurations is preserved under moderate tension, hence justifying the elastic behavior of carbon nanotubes in the axial traction regime.