Torsional buckling of carbon nanotubes based on nonlocal elasticity shell models

Abstract

This paper investigates size-effects in the torsional response of single walled carbon nanotubes (SWCNTs) by developing a modified nonlocal continuum shell model. The purpose is to facilitate the design of devices based on SWCNT torsion by providing a simple, accurate and efficient continuum model that can predict the corresponding buckling loads. To this end, Eringen’s equations of nonlocal elasticity are incorporated into the classical models for torsion of cylindrical shells given by Timoshenko and Donnell. In contrast to the classical models, the nonlocal model developed here predicts non-dimensional buckling torques that depend on the values of certain geometric parameters of the CNT, allowing for the inclusion of size-effects. Molecular dynamics simulations of torsional buckling are also performed and the results of which are compared with the classical and nonlocal models and used to extract consistent values of shell thickness and the nonlocal elasticity constant (e0). A thickness of 0.85 Å and nonlocal constant values of approximately 0.8 and 0.6 for armchair and zigzag nanotubes respectively are recommended for torsional analysis of SWCNTs using nonlocal shell models. The size-dependent nonlocal models together with molecular dynamics simulations show that classical shell models overestimate the critical buckling torque of SWCNTs and are not suitable for modeling of SWCNTs with diameters smaller than 1.5 nm.