Assessment of continuum mechanics models in predicting buckling strains of single-walledcarbon nanotubes

Abstract

This paper presents an assessment of continuum mechanics (beam and cylindrical shell)models in the prediction of critical buckling strains of axially loaded single-walled carbonnanotubes (SWCNTs). Molecular dynamics (MD) simulation results for SWCNTs withvarious aspect (length-to-diameter) ratios and diameters will be used as the referencesolutions for this assessment exercise. From MD simulations, two distinct buckling modesare observed, i.e. the shell-type buckling mode, when the aspect ratios are small, and thebeam-type mode, when the aspect ratios are large. For moderate aspect ratios, theSWCNTs buckle in a mixed beam–shell mode. Therefore one chooses either thebeam or the shell model depending on the aspect ratio of the carbon nanotubes(CNTs). It will be shown herein that for SWCNTs with long aspect ratios, thelocal Euler beam results are comparable to MD simulation results carried out atroom temperature. However, when the SWCNTs have moderate aspect ratios, itis necessary to use the more refined nonlocal beam theory or the Timoshenkobeam model for a better prediction of the critical strain. For short SWCNTs withlarge diameters, the nonlocal shell model with the appropriate small length scaleparameter can provide critical strains that are in good agreement with MD results.However, for short SWCNTs with small diameters, more work has to be done torefine the nonlocal cylindrical shell model for better prediction of critical strains.