Axially Compressive Deformation Mechanisms of Single- and Multi-Walled Carbon Nanotubes via Finite Element Analysis

A modified finite element method is presented and finite element simulations are performed on single-, double- and multi-walled carbon nanotubes to investigate their axially compressive buckling behaviors. The dependence of carbon nanotubes' axial buckling behaviors with respect to their physical dimensions is investigated by prescribing the relations of the critical buckling load and strain to the diameter, length of carbon nanotubes. In addition, the postbuckling responses are obtained for various carbon nanotubes. The simulation results show that larger tube diameter leads to higher buckling load until a stable value is reached, whereas larger tube length and length-to-radius ratio lead to lower buckling axial strains. At the same time, the applicability of the present modified finite element method to carbon nanotubes with various length-to-radius ratios is examined. The more extensive applicability of finite element method is revealed by comparing with the classical elastic shell theory, Euler column buckling theory and molecular dynamics simulation. And finally, the effects of numbers of layers on the buckling loads and axial strains of multi-walled carbon nanotubes are also examined. It is shown that the more layers multi-walled carbon nanotubes have, the higher buckling load is required while the smaller critical axial strain is demanded.