Mechanics of axial compression of single and multi-wall carbon nanotubes

A recently developed procedure for modeling the deformation of single and multi-wall carbon nanotubes [13,14] is applied to nanotube buckling and post-buckling under axial compression. Critical features of the model, which is grounded in elastic shell theory, include identification of (a) an appropriate elastic modulus and thickness pair matching both the wall stretching and bending resistances of the single atomic layer nanotube walls, and (b) a sufficiently stiff interwall van der Waals potential to preserve interwall spacing in locally buckled MWNTs, as is experimentally observed. The first issue is illustrated by parametric buckling studies on a SWNT and comparisons to a corresponding MD simulation from the literature; results clearly indicating the inadequacy of arbitrarily assigning the shell thickness to be the equilibrium spacing of graphite planes. Details of the evolution of local buckling patterns in a nine-walled CNT are interpreted based on a complex interplay of local shell buckling and evolving interwall pressure distributions. The transition in local buckling wavelengths observed with increasing post-buckling deformation is driven by the lower energy of a longer-wavelength, multiwall deformation pattern, compared to the shorter initial wavelength set by local buckling in the outermost shell. This transition, however, is contingent on adopting a van der Waals interaction sufficiently stiff to preserve interlayer spacing in the post-buckled configuration.