Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading

Abstract

This paper describes an investigation into elastic buckling of an embedded multi-walled carbon nanotube under combined torsion and axial loading, which takes account of the radial constraint from the surrounding elastic medium and van der Waals force between two adjacent tube walls. Depending on the ratio of radius to thickness, the multi-walled carbon nanotubes discussed here are classified as thin, thick, and nearly solid. Critical buckling load with the corresponding mode is obtained for multi-walled carbon nanotubes under combined torsion and axial loading, with various values of the radius to thickness ratio and surrounded with different elastic media. The study indicates that the buckling mode (m, n) of an embedded multi-walled carbon nanotube under combined torsion and axial loading is unique and it is different from that with axial compression only. New features for the buckling of an embedded multi-walled carbon nanotube under combined torsion and axial loading and the meaningful numerical results are useful in the design of nanodrive device, nanotorsional oscillator and rotational actuators, where multi-walled carbon nanotubes act as basic elements.

Dynamic shell buckling behavior of multi-walled carbon nanotubes embedded in an elastic medium

“…The pressure p d exerted on the outermost tube caused by the surrounding elastic medium [4,9] is described as:…”

“…In the present model, the Whitney-Riley model is used to determine the spring constant d. As that used by Wang et al [4], the surrounding elastic medium is regarded as a hollow cylinder with inner radius R N and outer radius r m , and the spring constant d is determined as:…”

“…)×0.34 nm [11,12,15], k =1, 2, …, N, E m =2.03 GPa and v m =0.33 for the surrounding elastic medium [4,17].…”

“…Mechanical behaviors of CNTs or CNTs in various surroundings have been widely investigated by experiments, molecular dynamic simulations and continuum mechanics models [3][4][5][6]. For example, Yakobson et al [7] studied the axial compressive buckling of SWNTs and found that the continuum shell model predicted well all the changes of buckling patterns displayed by molecular dynamics simulations.…”

Dynamic buckling behavior of multi-walled carbon nanotubes subjected to step axial loading

“…, and the innermost tube, respectively. As used in literatures [11,17,18,23,24] , an approximate linearized relation is adopted to model the effect of van der Waals forces between adjacent tubes of MWNTs in this paper: …”