Single-walled carbon nanotube modelling based on one- and two-dimensional Cosserat continua

This research aims to study the mechanical properties of single-walled carbonnanotubes. In order to overcome the difficulties of spanning multi-scales fromatomistic field to macroscopic space, the Cauchy-Born rule is applied to link thedeformation of atom lattice vectors at the atomic level with the materialdeformation in a macro continuum level. Single-walled carbon nanotubes aremodelled as Cosserat surfaces, and modified shell theory is adopted where adisplacement field-independent rotation tensor is introduced, which describes therotation of the inner structure of the surface, i.e. micro-rotation. Empiricalinteratomic potentials are applied so that stress fields and modulus fields can becomputed by the derivations of potential forms from displacement fields androtation fields. A finite element approach is implemented. Results of simulationsfor single-walled carbon nanotubes under stretching, bending, compression andtorsion are presented. In addition, Young’s modulus and Poisson ratio for graphitesheet and critical buckling strains for single-walled carbon nanotubes arepredicted in this research.