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In the present paper, a temperature-dependent meshless numerical frameworkbased on the thermo-related quasi-continuum constitutive model is developed forpredicting the thermal mechanical properties of single-walled carbon nanotubes(SWCNTs) at finite temperature. The extended thermal-related higher orderCauchy-Born (THCB) rule included second order deformation gradient relates thedeformation of bond vectors of the atomic system and that of the continuousmedium, which can capture the curvature effect of carbon nanotubes (CNTs)conveniently. Helmholtz free energy is employed to allow for the thermal effectof SWCNTs. In the meshless numerical implementations of the theory, the Newtoniteration method is applied to find the equilibrium configuration of a SWCNTsubjected to large deformation at a prescribed temperature only with the nodaldisplace parameters as optimization variables. The finite deformation behaviorsof armchair and zigzag SWCNTs under axial compression and torsion are tested.It is shown that the simulation results are in good agreement with thoseobtained by molecular dynamic methods even with fewer meshless nodes used.

Meshless simulation for thermo-mechanical properties of single-walled carbon nanotubes based on the thermal-related higher order Cauchy-Born rule