Column buckling of multiwalled carbon nanotubes with interlayer radial displacements

An elastic model is presented for column buckling of a multiwalled carbon nanotube embedded within an elastic medium. The emphasis is placed on the role of interlayer radial displacements between adjacent nanotubes. In contrast to an existing model which treats the entire multiwalled nanotube as a single column, the present model treats each of the nested tubes as an individual column interacting with adjacent nanotubes through the intertube van der Waals forces. Based on this model, a condition is derived in terms of the parameters describing the van der Waals interaction, under which the effect of the noncoincidence of all deflected column axes is so small that it does not virtually affect the critical axial strain. In particular, this condition is met for carbon multiwalled nanotubes provided that the half-wavelength of the buckling mode is much larger than the outermost diameter. In this case, the critical axial strain can be predicted correctly by the existing single-column model. On the other hand, the existing model could overestimate the critical axial strain when the half-wavelength of the buckling mode is close to or smaller than the outermost radius.