Effective Wall Thickness of Single-Walled Carbon Nanotubes for Multi-Scale Analysis: The Problem and a Possible Solution

  • L. C. Zhang
  • C. Y. Wang
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 13)


Continuum mechanics models have been used to characterize the mechanical behaviour of carbon nanotubes, but their validity down to the nanometer scale has not been fully verified. A typical example is the effective wall thickness of single-walled carbon nanotubes (SWCNTs), which has not been well defined after years of effort. This paper proposes a sufficient condition for determining the effective wall thickness h and Young's modulus E of an SWCNT using in-plane stiffness, K in-plane, torsion stiffness, D torsion, bending stiffness, D bending, and off-plane torsion stiffness, K torsion, as the independent elastic constants of a continuum model. The paper concludes that when the Vodenitcharova-Zhang's necessary condition and D bending/K in-plane = D torsion/K torsion are satisfied, the intersect of D bending and K in-plane curves in the E–h plane will determine a unique h, and in turn, leads to a defined E. For SWCNT (10, 10), h≈ 0.1 nmandE≈3.5TPa.


Carbon Nanotubes Atomistic Simulation Effective Thickness Plane Curf Radial Breathing Mode 
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Copyright information

© Springer Science+Business Media, B.V. 2009

Authors and Affiliations

  • L. C. Zhang
    • 1
  • C. Y. Wang
    • 1
  1. 1.School of Aerospace, Mechanical and Mechatronic EngineeringThe University of SydneySydneyAustralia

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