Abstract:

In this paper, the torsional buckling of a multi-wall carbon nanotube embedded in elastic medium is investigated by considering the effects of the surrounding elastic medium and the van der Waals force. Then, based on the theory of continuum mechanics, a multi-layer elastic shell model is presented to analyze the torsional buckling of the nanotube. Moreover, an approximate method is suggested based on the proposed model, which substitutes an elastic shell with fewer layers for the multi-wall carbon nanotube. In particular, when the radius-to-thickness ratio of a N-wall carbon nanotube is more than 5, the nanotube may be approximately equivalent to a singlewall elastic shell, and the effective bending stiffness and thickness of the N-wall nanotube are （10N- 9） and N times that of the single-wall nanotube, respectively. The critical buckling torque of the multi-wall carbon nanotube is finally estimated by numerical calculation. The results demonstrate that the proposed approximate method is simple and effective.

Key words: nanotube, buckling, elastic medium, Winkler model, van der Waals force