Numerical simulation for finite deformation of single-walled carbon nanotubes at finite temperature using temperature-related higher order Cauchy-Born rule based quasi-continuum model

In the present study, a meshless computational framework for simulating the large deformation behaviors of single-walled carbon nanotubes (SWCNTs) at finite non-zero temperatures is established based on the so-called temperature-related higher order Cauchy-Born rule (THCB rule) where the second-order deformation gradient is involved in the kinematic description of the deformation of SWCNTs. The Helmholtz free energy is used as the thermodynamic potential and the local harmonic approximation (LHA) is adopted to construct the nanoscale quasi-continuum constitutive model. The proposed numerical approach is then applied to four numerical examples under different loading conditions. It is found that the results obtained by the proposed numerical framework agree well with those from molecular dynamics simulations.