Mechanical properties of single-walled carbon nanotubes based on higher order Cauchy–Born rule

A nanoscale continuum theory is established based on the higher order Cauchy–Born rule to study the mechanical properties of carbon nanotubes. The theory bridges the microscopic and macroscopic length scale by incorporating the second-order deformation gradient into the kinematic description. Moreover, the interatomic potential and the atomic structure of carbon nanotube are incorporated into the proposed constitutive model in a consistent way. Therefore the single-walled carbon nanotube can be viewed as a macroscopic generalized continuum with microstructure. Based on the present theory, the energy and the size dependent mechanical properties of SWNT and graphite are predicted and compared with the existing experimental and theoretical data.