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.
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May 2011
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A Finite Element Analysis of Single-Walled Carbon Nanotube Deformation
Chao Fang,
Chao Fang
Sibley School of Mechanical and Aerospace Engineering,
Cornell University
, Ithaca, NY 14853
Search for other works by this author on:
Ajeet Kumar,
Ajeet Kumar
Sibley School of Mechanical and Aerospace Engineering,
Cornell University
, Ithaca, NY 14853
Search for other works by this author on:
Subrata Mukherjee
Subrata Mukherjee
Professor
Fellow ASME
Sibley School of Mechanical and Aerospace Engineering,
Cornell University
, Ithaca, NY 14853
Search for other works by this author on:
Chao Fang
Sibley School of Mechanical and Aerospace Engineering,
Cornell University
, Ithaca, NY 14853
Ajeet Kumar
Sibley School of Mechanical and Aerospace Engineering,
Cornell University
, Ithaca, NY 14853
Subrata Mukherjee
Professor
Fellow ASME
Sibley School of Mechanical and Aerospace Engineering,
Cornell University
, Ithaca, NY 14853J. Appl. Mech. May 2011, 78(3): 034502 (7 pages)
Published Online: February 17, 2011
Article history
Received:
June 14, 2010
Revised:
December 3, 2010
Posted:
December 8, 2010
Published:
February 17, 2011
Online:
February 17, 2011
Citation
Fang, C., Kumar, A., and Mukherjee, S. (February 17, 2011). "A Finite Element Analysis of Single-Walled Carbon Nanotube Deformation." ASME. J. Appl. Mech. May 2011; 78(3): 034502. https://doi.org/10.1115/1.4003191
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