Coupling of Extension and Twist in Single-Walled Carbon Nanotubes

This paper presents a study of the deformation behavior of single-walled carbon nanotubes (SWNTs) subjected to extension and twist. The interatomic force description is provided by the Tersoff-Brenner potential for carbon. The rolling of a flat graphene sheet into a SWNT is first simulated by minimizing the energy per atom, the end result being the configuration of an undeformed SWNT. The Cauchy-Born rule is then used to connect the atomistic and continuum descriptions of the deformation of SWNTs, and leads to a multilength scale mechanics framework for simulating deformation of SWNTs under applied loads. Coupled extension and twist of SWNTs is considered next. As an alternative to the Cauchy-Born rule for coupled extension-twist problems, a direct map is formulated. Analytic expressions are derived for the deformed bond lengths using the Cauchy-Born rule and the direct map for this class of deformations. Numerical results are presented for kinematic coupling, for imposed extension and imposed twist problems, using the Cauchy-Born rule as well as the direct map, for representative chiral, armchair and zig-zag SWNTs. Results from both these approaches are carefully compared.