Continuum Shell Model for Buckling of Single-Walled Carbon Nanotubes with Different Chiral Angles

In this paper, an equivalent thick cylindrical shell model is proposed for the buckling analysis of short single-walled carbon nanotubes (SWCNTs) with allowance for different chiral angles. Extensive, molecular dynamics (MD) simulations are first performed using the adaptive intermolecular reactive bond order potential to determine the critical buckling loads/strains. The MD simulations buckling results are then used as reference solutions to calibrate the properties of the thick cylindrical shell model. Central to this development is the establishment of an empirical expression for the Young's modulus that is a function of both the diameter and the chiral angle of the SWCNT. For the shell model, we have assumed that the Poisson ratio upsilon = 0.19 and the shell thickness h = 0.066 nm. It will be shown that the proposed shell model furnishes good estimates of the critical buckling loads for SWCNTs with different chiral angles. The critical buckling strains are also evaluated from the critical buckling load with the aid of the stress-strain relation of SWCNTs.