Abstract2018-05-24T12:52:58+00:00

Effective coarse-grained simulations of super-thick multi-walled carbon nanotubes under torsion

Author (s): Jian Zou, Xu Huang, Marino Arroyo, and Sulin Zhang
Journal: Journal of Applied Physics

Volume: 5, Issue 3
Pages: 33516 – 9
Date: 2009

Abstract:



JAP-JZx-XHx-MAB-SZx-1


Effective coarse-grained simulations of super-thick multi-walled carbon nanotubes under torsion
Jian Zou, Xu Huang, Marino Arroyo, and Sulin Zhang

Under torsion and beyond the buckling point, multi-walled carbon nanotubes (MWCNTs) develop a periodic wave-like rippling morphology. Here, it is shown that torsional rippling deformations can be accurately described by a simple sinusoidal shape function.  Combining this observation with the classical Rayleigh-Ritz method, we develop a coarse-grained minimal model that reproduces the complex nonlinear mechanics of thick MWCNTs under torsion predicted by large-scale simulations. Furthermore, the model presented here allows us to simulate super-thick tubes, inaccessible by direct numerical simulation, with a very low computational cost. With this coarse-grained model, we show from an energetic analysis that the rippling deformation is a result of in-plane strain energy relaxation, penalized by the increase of the interlayer van der Waals interaction energy.  Our simulations reveal that the torsional response of MWCNTs with up to 100 layers approximately follows a simple bilinear law, where the turning point of the torsional rigidity identifies the bifurcation torsional strain.  We further show that the ratio of the torsional rigidities in the pre- and post-bulking regimes is nearly a constant of 0.681, independent of the tube radius.  In contrast, the bifurcation torsional strain depends on the tube radius with a power-law.  We also find that the wave number in the circumferential direction linearly increases with tube radius, while the wavelength monotonically increases with tube radius, and approaches a constant value in the limit of infinitely thick MWCNTs.  The bilinear constitutive relation, together with the scaling law of the bifurcation torsional strain, furnishes a simple nonlinear beam theory, which facilitates the analysis of MWCNTs bundles and networks.

  
  

Bibtex:

@article{:/content/aip/journal/jap/105/3/10.1063/1.3074285,
   author = "Zou, J.; Huang, X.; Arroyo, M. and Zhang, S.",
   title = "Effective coarse-grained simulations of super-thick multi-walled carbon nanotubes under torsion",
   journal = "Journal of Applied Physics",
   year = "2009",
   volume = "105",
   number = "3", 
   eid = 033516,
      url = "http://scitation.aip.org/content/aip/journal/jap/105/3/10.1063/1.3074285",
   doi = "http://dx.doi.org/10.1063/1.3074285" 
}