Finite element analysis of single-walled carbon nanotubes based on a rod model including in-plane cross-sectional deformation

Abstract

This paper presents a finite element method (FEM) implementation of a rod model for single-walled carbon nanotubes (SWNT), 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 cross-section 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. The material parameters of this rod model are estimated using both the density functional based tight binding (DFTB) method as well as using the Tersoff–Brenner inter-atomic potential. A discrete variational approach is combined with a Newton-Raphson iterative method to solve the geometrically nonlinear rod model. Several numerical results are presented illustrating coupling between different deformation modes of a SWNT as well as its Euler buckling.