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Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models

Publication Type:

Journal Article


Computational Materials Science, Elsevier, Volume 48, p.736-742 (2010)



This paper investigates size-effects in the torsional response of single walled carbon nanotubes (SWCNTs)
by developing a modified nonlocal continuum shell model. The purpose is to facilitate the design of
devices based on SWCNT torsion by providing a simple, accurate and efficient continuum model that
can predict the corresponding buckling loads. To this end, Eringen’s equations of nonlocal elasticity are
incorporated into the classical models for torsion of cylindrical shells given by Timoshenko and Donnell.
In contrast to the classical models, the nonlocal model developed here predicts non-dimensional buckling
torques that depend on the values of certain geometric parameters of the CNT, allowing for the inclusion
of size-effects. Molecular dynamics simulations of torsional buckling are also performed and the results
of which are compared with the classical and nonlocal models and used to extract consistent values of
shell thickness and the nonlocal elasticity constant (e0). A thickness of 0.85 Å and nonlocal constant values
of approximately 0.8 and 0.6 for armchair and zigzag nanotubes respectively are recommended for
torsional analysis of SWCNTs using nonlocal shell models. The size-dependent nonlocal models together
with molecular dynamics simulations show that classical shell models overestimate the critical buckling
torque of SWCNTs and are not suitable for modeling of SWCNTs with diameters smaller than 1.5 nm.

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