Torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium

This paper investigates torsional buckling of a multi-wall carbon nanotube embedded in an elastic medium. The effects of surrounding elastic medium and van der Waals forces from adjacent nanotubes are taken into account. Using continuum mechanics, an elastic laminated shell model is presented to study the torsional buckling of a multi-wall carbon nanotube embedded in an elastic medium. A laminated cylinder composed of a multi-wall carbon nanotube and a surrounding elastic medium is used to describe the effect of elastic medium on the multi-wall carbon nanotubes. According to the ratio of radius-to-thickness, multi-wall carbon nanotubes discussed here are classified into three cases: thin, thick, and nearly solid. The critical shear stress and the torsional buckling mode are calculated for various radius-to-thickness ratios and elastic medium effects. Results carried out show that the buckling mode (m, n) corresponding the critical shear stress is sole, which is obviously different from the axially compressed buckling of multi-wall carbon nanotubes. The investigation on torsional buckling of multi-wall carbon nanotubes embedded in an elastic medium in this paper may be used as a useful reference for the designs of nano-oscillators and actuators in which multi-wall carbon nanotubes act as torsional springs.