The effect of dimensional factors on buckling of multiwall carbon nanotubes

Based on a multiple-shell model, a comprehensive investigation has been performed on the effect of three dimensional factors, i.e., aspect ratio, the innermost radius, and the number of layers, on buckling behavior of multiwall carbon nanotubes (MWCNTs) under axial compression or radial pressure. In contrast to previous shell models, which use the single Donnell equation [Wang , ASME J. Appl. Mech. 71, 622 (2004)] and thus are only adequate for buckling of MWCNTs of relatively small aspect ratio (e.g., not larger than 10), the present shell model based on the simplified Flugge equation [Wang , ASME J. Appl. Mech. 71, 622 (2004)] allows for the study of buckling behavior of MWCNTs without any limitation on their aspect ratios. In addition, the pressure dependence of the interlayer van der Waals interaction coefficient (defined as the second derivative of the interlayer potential energy-interlayer spacing relation) has been considered for pressure-induced buckling of MWCNTs. The relevance of the present shell model for buckling of MWCNTs has been confirmed by the good agreement between the present shell model and available discrete models or experiments. Here, distinct buckling behaviors under axial compression or radial pressure are identified for long and short MWCNTs, separated by a certain critical value of aspect ratio. On the other hand, while the critical buckling load usually changes monotonically with the innermost radius an optimum value of the number of layers associated with the maximum critical buckling pressure is obtained for MWCNTs under radial pressure. In particular, the present shell model shows that the three dimensional factors effecting buckling of MWCNTs are generally interacting with, rather than being independent of, one another. (c) 2007 American Institute of Physics.