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Technical Briefs

A Finite Element Analysis of Single-Walled Carbon Nanotube Deformation

[+] Author and Article Information
Chao Fang, Subrata Mukherjee

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853

Ajeet Kumar1

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853

1

Present address: Postdoctoral Research Associate, Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455.

J. Appl. Mech 78(3), 034502 (Feb 17, 2011) (7 pages) doi:10.1115/1.4003191 History: Received June 14, 2010; Revised December 03, 2010; Posted December 08, 2010; Published February 17, 2011; Online February 17, 2011

Chandraseker (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., , 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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Kinematic description of a Cosserat rod (1)

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Figure 2

Variation of various moduli with generalized strain

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Figure 3

Deforming trajectories of a cantilever beam subjected to an increasing end moment

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Figure 4

Comparison of simple beam deflection (left) with carbon nanotube deflection (right)

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Figure 5

Comparison of deflections of a materially nonlinear CNT with materially linear and simple beam

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Figure 6

Zoomed-in version of part of Fig. 5

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Figure 7

Three dimensional deflection of a materially nonlinear CNT. The left figure shows the deformed configuration of a CNT while the right figure is a zoomed-in part of the right end.

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