Chirality-Dependent Mechanical Behavior of Carbon Nanotubes Based on an Anisotropic Elastic Shell Model

Motivated by recently reported chirality-dependent mechanical phenomena of small-radius carbon nanotubes, an anisotropic elastic shell model is developed in the present paper for small-radius single-walled carbon nanotubes. Due to curvature-derived elastic anisotropy, small-radius single-walled carbon nanotubes are better described by anisotropic plane-stress relations rather than graphite sheets of hexagonal symmetry which are governed by an isotropic plane-stress relation. Based on an orthotropic plane-stress elastic relation for zigzag and armchair single-walled carbon nanotubes, the suggested model is formulated for chiral single-walled carbon nanotubes of arbitrary chiral angle through a small-angle (less than pi/12) rotation of the coordinate system. The results obtained show that the suggested anisotropic shell model can explain the chirality-dependent mechanical phenomena reported in the recent literature, and could be used to study chirality-dependent mechanical behavior of multi-walled carbon nanotubes of smaller innermost radii.