Abstract

This research aims to study the mechanical properties of single-walled carbon
nanotubes. In order to overcome the difficulties of spanning multi-scales from
atomistic field to macroscopic space, the Cauchy-Born rule is applied to link the
deformation of atom lattice vectors at the atomic level with the material
deformation in a macro continuum level. Single-walled carbon nanotubes are
modelled as Cosserat surfaces, and modified shell theory is adopted where a
displacement field-independent rotation tensor is introduced, which describes the
rotation of the inner structure of the surface, i.e. micro-rotation. Empirical
interatomic potentials are applied so that stress fields and modulus fields can be
computed by the derivations of potential forms from displacement fields and
rotation fields. A finite element approach is implemented. Results of simulations
for single-walled carbon nanotubes under stretching, bending, compression and
torsion are presented. In addition, Young’s modulus and Poisson ratio for graphite
sheet and critical buckling strains for single-walled carbon nanotubes are
predicted in this research.