A rod model for three dimensional deformations of single-walled carbon nanotubes

A continuum model for single-walled carbon nanotubes (SWCNT) is presented which is based on an extension to the special Cosserat theory of rods (Kumar and Mukherjee, 2011). The model allows deformation of a nanotube's lateral surface in a one dimensional framework and hence is an efficient substitute to the commonly used two dimensional shell models for nanotubes. The model predicts a new coupling mode in chiral nanotubes - coupling between twist and cross-sectional shrinkage implying that the three deformation modes (extension, twist and cross-sectional shrinkage) are all coupled to each other. Atomistic simulations based on the density functional based tight binding method (DFTB) are performed on a (9, 6) SWCNT and the simulation data is used to estimate material parameters of this rod model. A peculiar behavior of the nanotube is observed when it is axially stretched - induced rotation of each cross-section is equal in magnitude but opposite to that of its two neighboring cross-sections. This is shown to be an effect of relative shift/inner- displacement between the two SWCNT sub-lattices.