Energy and mechanical properties of single-walled carbon nanotubes predicted using the higher order Cauchy-Born rule

Based on the higher order Cauchy-Born rule, a continuum-based constitutive model, which taking the interatomic potentials and atomic microstructure of carbon nanotubes into consideration, is presented for the analysis of the mechanical properties of carbon nanotubes. With the use of Tersoff-Brenner potential, the influences of the potential parameters, tube diameters, chirality and the inner displacement on the energies, the axial Young’s moduli, the circular elastic moduli of graphite and single-walled carbon nanotubes as well as the bending stiffness of SWNT are investigated. The results obtained are in good agreement with that of molecular dynamics.

Figure 1

The representative cell of the atom $i$.

Figure 2

The energy relative to graphite ($\mathrm{kg}{\mathrm{nm}}^2∕{\mathrm{s}}^2$ per carbon atom) as a function of tube radius for $BP1$ and $BP2$.

Figure 3

The axial Young’s modulus (with inner displacement relaxation) versus tube radius for $BP1$ and $BP2$.

Figure 4

The nonrelaxation axial Young’s modulus versus tube radius for $BP1$ and $BP2$.

Figure 5

The circular modulus (with inner displacement relaxation) versus tube radius for $BP1$ and $BP2$.

Figure 6

The nonrelaxation circular modulus versus tube radius for $BP1$ and $BP2$.

Figure 7

Schematic illustration of bending SWNT.

Figure 8

The total strain energy (in dimensionless units) of SWNT (13,0) as a function of the bending angle.