Examination of beam and cylindrical shell models for buckling analysis of carbon nanotubes

![CDATA[This paper examines the beam and cylindrical shell models proposed for the prediction of critical buckling strains of axially loaded single-walled carbon nanotubes (SWCNTs). Molecular dynamics (MD) simulations results for SWCNTs with various aspect (length-to-diameter) ratios and diameters will be used as reference solutions to assess the models. From MD simulations, two distinct buckling modes are observed, i.e. the shell-type buckling mode when the aspect ratios are small and the beam-type mode when the aspect ratios are large. For moderate aspect ratios, the SWCNTs buckle in a mixed beam-shell mode. Therefore the selection of beam or shell models depends on the aspect ratio of the carbon nanotubes. It will be shown herein that for SWCNTs with long aspect rations, the local Euler beam results are comparable to MD simulation results carried out at room temperature. However, when the SWCNTs have moderate aspect ratios, it is necessary to use the more refined nonlocal beam theory or the Timoshenko beam model for a better prediction of the critical strain. For short SWCNTs with large diameters, the nonlocal shell model with the appropriate small length scale parameter can provide critical strains that are in good agreement with MD results. But for short SWCNTs with small diameters, more work has to be done to refine the nonlocal cylindrical shell model for better prediction of critical strains.]]