This paper elucidates the buckling behavior of carbon nanotubes (CNTs) under bending. CNTs are modeled as continuous thin-wall circular tubes, and their buckling is governed by equations that take into account of the sectional Brazier effect and non-uniform structural deformation. The CNT governing equations (fourth-order ordinary differential nonlinear equations with integral conditions) are solved by introducing a continuation algorithm. In addition, the buckling behavior of CNTs under bending is simulated with objective molecular dynamics (OMD). The atomistic simulations are used to verify the continuum results. We show that there exist low- and high-strain phases during the bending process of CNTs, and the transition in between may divide the whole bending process into three stages: low-curvature stage, mixed-curvature stage and high-curvature stage. Ripples are generated on the CNT surfaces before the formation of kinks. Compared to single-walled CNTs (SWCNTs), hydrogen-filled CNTs have a longer mixed-strain stage owing to the presence of internal pressure, and are therefore more inclined to exhibit a ripple morphology. Our results offer better understanding of the buckling behavior of CNTs, and may open up new opportunities for the design and applications of novel CNT-based nanoelectronics.
Bibliographical noteFunding Information:
The authors gratefully acknowledge financial supports from National Natural Science Foundation of China , 11172079 and 11572099 ; Program for New Century Excellent Talents in University , NCET-11-0807 ; Natural Science Foundation of Heilongjiang Province of China, A2015002 ; the Fundamental Research Funds for the Central Universities , HIT.BRETIII.201209 . JA and TD acknowledge support from the National Science Foundation grant CMMI-1332228 , and NASA grant NNX16AE03G . Meanwhile, we thank Dr. B. Li in Shanghai Jiao Tong University for his great help.
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