Interaction diagrams for carbon nanotubes under combined shortening–twisting

A theoretical investigation on the strength and stiffness of carbon nanotubes (CNTs) under combined shortening and twisting strains is presented. CNTs with similar length-to-diameter aspect ratios, L/D, but different atomic structures (zig-zag, armchair and chiral) have been selected. Molecular dynamics (MD) simulations have been performed to study the critical buckling behaviour and the pre-critical and post-critical stiffness of CNTs under combined shortening–twisting conditions. The main results are presented in the form of interaction diagrams between the critical strain and the critical angle of twist per unit of length. An interaction equation is proposed and validated by comparison with the MD results. If shortening is more dominant than twisting, the strain energy at the onset of buckling drops considerably with the increase of the twisting–shortening rate. If twisting is more influential than shortening, the energy at the onset of buckling decreases very slowly with the twisting–shortening rate. We also found an interaction factor of 1.5 for CNTs under combined shortening–twisting, which is much lower than the value 2.0 commonly adopted for circular tubes at macro-scale. We conclude that CNTs are much more sensitive to buckling under shortening–twisting interaction than macro-scale tubes.