Postbuckling prediction of double-walled carbon nanotubes under hydrostatic pressure

Abstract

An elastic double-shell model is presented for the buckling and postbuckling of a double-walled carbon nanotube subjected to external hydrostatic pressure. The analysis is based on a continuum mechanics model in which each tube of a double-walled carbon nanotube is described as an individual elastic shell and the interlayer friction is negligible between the inner and outer tubes. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The van der Waals interaction between the inner and outer nanotubes and the nonlinear prebuckling deformations of the shell are both taken into account. A boundary layer theory of shell buckling is extended to the case of double-walled carbon nanotubes under hydrostatic pressure. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the single-walled carbon nanotube has a stable postbuckling path, whereas the double-walled carbon nanotube has an unstable postbuckling behavior due to the presence of van der Waals interaction forces.