Torsional buckling and postbuckling equilibrium path of double-walled carbon nanotubes

Based on a continuum elastic double-shell model in which each tube of a double-walled carbon nanotube is described as an individual elastic shell, involving the van der Waals interaction between the inner and outer nanotubes, the governing equations for the buckling and postbuckling behavior of double-walled carbon nanotubes subjected to torsional load are presented based on the Karman–Donnell-type nonlinear differential equations. Applying the boundary-layer theory of shell and employing singular perturbation technique, accurate solutions are obtained to determine the buckling loads and postbuckling equilibrium paths. Through detailed calculations, main postbuckling characteristics, i.e. connections of the angle of twist, axial end-shortening and transverse deflection with applied torque, are clarified for a range of nanotube geometrics. Results reveal that under the torsional load double-walled carbon nanotube has an unstable postbuckling behavior. And it is confirmed that the postbuckling equilibrium path becomes higher when the nanotube becomes thinner.