Dual ideal shear strengths for chiral single-walled carbon nanotubes

By considering a single-walled carbon nanotube (SWCNT) as a two-dimensional elastica obtained from the roll-up of a graphene sheet into a circular tube, the present paper develops a precise well-posed continuum theory for describing the entire torsional behavior of SWCNTs from an initial unloaded state through their ultimate levels of loading. In addition, the proposed approach can capture the dual ideal shear strengths as well as the asymmetrical behavior of chiral tubes with respect to the direction of the applied torsional loading. The theory incorporates a highly nonlinear constitutive equation which provides information about the nanoscopic morphological parameters of the tubes. As it will be shown, the longitudinal and twist deformations are coupled. Accordingly, a parameter referred to as the torsion-induced extension will be defined.