A Finite Element Analysis of Single-Walled Carbon Nanotube Deformation

Chandraseker et al. (2009, “An Atomistic-Continuum Cosserat Rod Model of Carbon Nanotubes,” J. Mech. Phys. Solids, 57, pp. 932–958), in a 2009 JMPS paper, proposed an atomistic-continuum model, based on Cosserat rod theory, for deformation of a single-walled carbon nanotube (SWNT). This model allows extension and twist, as well as shear and bending (in two directions) of a SWNT. This present paper proposes a finite element method (FEM) implementation of the above mentioned Cosserat rod model for a SWNT, subjected, in general, to axial and transverse loads, as well as bending moments and torques. The resulting FEM implementation includes both geometric and material nonlinearities. Numerical results for several examples are presented in this paper. Finally, a recent experimental paper on SWNTs (Xu, Y-.Q., et al., 2009, “Bending and Twisting of Suspended Single-Walled Carbon Nanotubes in Solution,” ASAP Nano Lett., 9, pp. 1609–1614) is revisited herein. It is pointed out in the present paper that Xu et al. attempted to determine the bending stiffness of a SWNT from an experiment in which the dominant mode of deformation is stretching, not bending. (Their model, Euler–Bernoulli beam bending, should perhaps have been extended to include stretching.) As a result, their measured deflection is nearly insensitive to the bending modulus.