Abstract

This paper studies the mechanical properties of single-walled carbon nanotubes (SWCNTs). In order to overcome the difficulty 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 at a macro continuum level. SWCNTs are modelled as Cosserat surfaces, and the 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. the micro-rotation. Empirical interatomic potentials are employed, so that the force and modulus fields can be computed by the derivations of potential forms from the displacement and rotation fields. A finite element approach is implemented. The Young’s modulus is predicted for SWCNTs in the paper.