Keywords: torsional buckling, atomic-scale finite element, critical torsional angle, strain energy.

The excellent mechanical properties of carbon nanotubes (CNTs) have attracted enormous research interest for both science and technology applications. Their buckling behavior is an important topic for both experimental investigation and theoretical research. Compared with extensive experimental research on the buckling of CNTs under compression and bending, experimental studies on their torsional buckling are limited. The limited research on torsional buckling concentrates mainly on theoretical research via molecular dynamics (MD) and continuum mechanics. Even for the axial compression and tension of CNTs, MD simulation is so computationally expensive that it is difficult to scale up. Besides the great computational effort, MD simulation of torsional buckling involves other difficulties such as the realization of torque on an atomistic system and the large deformation around the spiral. There is some investigation based on continuum mechanics to study torsional buckling of CNTs. In the continuum models, the dependence of critical torsional angle and concrete configuration of buckled CNTs could hardly be achieved.

Liu et al. [1] proposed an atomic-scale finite element method. Using inter-atomic potential to consider the multi-body interactions, it is as accurate as molecular mechanics simulation and much faster than the conjugate gradient method. This paper employs it to study torsional buckling of single-walled carbon nanotubes (SWNTs). Dependence of critical torsional angle on the length of SWNTs with a fixed diameter is found to be consistent with conventional shell theory. Also, for armchair and zigzag SWNTs with fixed aspect ratios, the critical torsional angles are achieved and compared with conventional shell theory. A (13,0) SWNT is taken as an example of post-buckling. When the torsional angle is large enough, a spiral is initiated, its morphology changes abruptly, and there is a slight drop in the strain energy. After that the strain energy increases approximately linearly with respect to the torsional angle, and the spiral continues developing. The morphologies of twisted SWNT are presented in detail in the full paper.

1

B. Liu, Y. Huang, H. Jiang, S. Qu and K.C. Hwang, "The atomic-scale finite element method", Comput Methods Appl. Mech. Eng., 193, 1849-1864, 2004. doi:10.1016/j.cma.2003.12.037

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