Bending buckling behaviors of single- and multi-walled carbon nanotubes

The bending buckling behaviors of single- (SWCNTs), double- (DWCNTs) and multi-walled carbon nanotubes (MWCNTs) are investigated employing a modified finite element method (FEM). Extensive finite element simulations are carried out to investigate the buckling behaviors of SWCNTs, DWCNTs and MWCNTs under bending deformation. The computed results for SWCNTs agree well with atomistic simulations in the literature and the validation of the present modified FEM is confirmed successfully. Explicit relationships are established between the critical bending buckling curvature and the diameter of carbon nanotubes (CNTs). The variations of the bending load with the bending angle or curvature for CNTs with different geometrical parameters, such as tube diameter, length and chirality, are revealed amply. And the results are correlated with the buckled geometrical configurations. The significant influence of interlayer van der Waals (vdW) forces on the bending properties of MWCNTs is examined. And finally, the effects of the number of layers on the buckling load and critical bending angle of MWCNTs are also examined. A number of significant conclusions drawn from the extensive simulations are presented. It is shown that the present modified FEM is computationally fast and is an alternative efficient way to study the buckling and postbuckling of CNTs.