On the accuracy of shell models for torsional buckling of carbon nanotubes

This paper presents a study on the suitability of shell models to assess the buckling behaviour of single-walled carbon nanotubes (CNTs) under torsion. It is shown that the simultaneous use of both well known (i) Donnell shell model and (ii) uniform helix deflected shape (HDS) of CNTs, leads to incorrect values of the critical angle of twist per unit of length, as they do not match the results obtained from molecular dynamic simulations. Conversely, more sophisticated models, like the Sanders shell model (SSM) with non-uniform HDS is found to lead to correct results of critical angle of twist. It is established that there is a transitional aspect ratio (length-to-diameter ratio) that separates the group of short CNTs, mostly influenced by end conditions, from the group of long CNTs, mostly influenced by warping deformation. Based on the SSM with non-uniform HDS, straightforward analytical expressions to calculate the critical angle of twist are proposed for each of these groups. Despite its simplicity, the procedure presented is shown to give rather accurate results for a wide range of CNT lengths, diameter and chirality.