Determination of Non-local Elasticity Constants for the Torsional Buckling of Single-Wall Carbon Nanotubes Using Molecular Dynamics
F. Khademolhosseini, R.K.N.D. Rajapakse, A. Nojeh
University of British Columbia, CA
Keywords: carbon nanotubes, torsion, buckling, non-local elasticity
Abstract:Recently, devices have been developed which use Carbon Nanotubes (CNTs) as torsional spring elements. In order to define the range of applicability of CNTs in such devices, it is important to fully understand their torsional response, and to investigate failure modes such as the torsional buckling limit. Currently available models are inaccurate as they are unable to account for the size effects that inevitably exist in such devices. We propose a modified nonlocal continuum shell model for the torsional buckling of CNTs. We have modified classical continuum models and incorporated basic concepts from nonlocal elasticity. Furthermore, we have performed molecular dynamics (MD) simulations on a range of Zigzag and Armchair nanotubes with different diameters. It is easily seen that compared to classical models, our modified nonlocal model provides a much better fit to MD simulation results. Based on our results, we propose a global thickness of 0.085 nm for CNTs subject to torsion. Values of the nonlocal constants are calculated as 0.6 and 0.8 for Zigzag and Armchair CNTs respectively. Through comparison of classic and modified non-local models we can see that classical approaches overestimate the critical buckling torque of CNTs by as much as 30 percent.