Elastic property and buckling behavior of carbon nanotubes

Abstract

This thesis is concentrated on the mechanical behavior of CNTs. For zigzag SWNT in compression, two constant longitudinal strains for laminar substructures are found to appear in a periodic way; while for armchair SWNT in compression, two constant transversal strains for laminar substructures are found to appear periodically, leading to the consideration of “spatial periodic strain.” An equilibrium relationship is established for the mechanics of SWNTs and an efficient approach is presented to investigate mechanical properties of SWNTs. The validity is demonstrated by comparing its calculation results with existing results. The AFEM is employed to study buckling behavior of CNTs under compression, bending and torsion. For axial buckling of SWNTs, both local and global buckling are investigated and two corresponding buckling zones are obtained. For the global buckling of SWNTs, both exponentially decaying and power functions can fit the critical strains very well. The empirical formulas show that their global buckling behavior gradually approaches that of an Euler column. For DWNTs, the simulation shows that the local buckling behavior can be explained very well by conventional shell theory. For axial post-buckling of CNTs, strain energy releases at morphology changes and varies approximately piecewise linearly. For bending buckling of SWNTs, kinks appear and the morphology change abruptly at certain bending angles. The strain energy grows initially as a quadratic function of bending angle, then increases gradually slowly, and finally changes approximately piecewise linearly. The simulation shows that the appearance of buckling reduces the slope of the strain energy curve and hence increases their flexibility. For torsional buckling of SWNTs, spiral appears and the morphology changes abruptly at certain torsional angles. The strain energy grows quadratically with the torsional angle and then changes approximately linearly after the first bifurcation. The dependence of critical torsional angle on the length is compared with the conventional shell theory.