Investigation of the thermo-mechanical properties of single-walled carbon nanotubes based on the temperature-related higher order Cauchy–Born rule

In the present study, a nanoscale quasi-continuum constitutive model for predicting the thermal-mechanical properties of single-walled carbon nanotubes (SWCNTs) and graphene sheet is established based on the interatomic potential and the temperature-related higher order Cauchy–Born rule. Helmholtz free energy is used as the corresponding thermodynamic potential. It is a function of some temperature-dependent lattice parameters that can be determined through an energy minimization process. As an application of the proposed quasi-continuum model, temperature dependency and curvature effect of the specific heat, the coefficient of thermal expansion (CTE) and the Young’s modulus of SWCNTs are investigated systematically. Numerical results obtained show the effectiveness of the proposed constitutive model.