A continuum mechanics nonlinear postbuckling analysis for single-walled carbon nanotubes under torque

Nonlinear buckling and postbuckling analysis of single-walled carbon nanotubes subjected to torsional load are examined by continuum mechanics elastic shell model. The boundary layer theory of shell buckling and the singular perturbation technique is applied to solve the governing equations based on the Karman–Donnell-type nonlinear differential equations. The buckling loads and postbuckling equilibrium paths are obtained theoretically. For more detailed descriptions on the postbuckling behaviors of single-walled carbon nanotubes, postbuckling relations between twist, end-shortening, transverse deflection and the torque are investigated for nanotubes with different geometric parameters. Numerical results obtained show that single-walled carbon nanotubes under the torsional load have unstable postbuckling behavior, and the postbuckling equilibrium path is higher for the thinner nanotube than that of the thicker nanotubes. Furthermore, a new conclusion drawn from the postbuckling analysis on single-walled carbon nanotubes with different Young's modulus and the wall thickness is significant to definite the mechanical parameters of single-walled carbon nanotubes.