Nonlinear buckling analyses of a small-radius carbon nanotube

Carbon nanotube (CNT) was first discovered by Sumio Iijima. It has aroused extensive attentions of scholars from all over the world. Over the past two decades, we have acquired a lot of methods to synthesize carbon nanotubes and learn their many incredible mechanical properties such as experimental methods, theoretical analyses, and computer simulations. However, the studies of experiments need lots of financial, material, and labor resources. The calculations will become difficult and time-consuming, and the calculations may be even beyond the realm of possibility when the scale of simulations is large, as for computer simulations. Therefore, it is necessary for us to explore a reasonable continuum model, which can be applied into nano-scale. This paper attempts to develop a mathematical model of a small-radius carbon nanotube based on continuum theory. An Isotropic circular cross-section, Timoshenko beam model is used as a simplified mechanical model for the small-radius carbon nanotube. Theoretical part is mainly based on modified couple stress theory to obtain the numerical solutions of buckling deformation. Meanwhile, the buckling behavior of the small radius carbon nanotube is simulated by Molecular Dynamics method. By comparing with the numerical results based on modified couple stress theory, the dependence of the small-radius carbon nanotube mechanical behaviors on its elasticity constants, small-size effect, geometric nonlinearity, and shear effect is further studied, and an estimation of the small-scale parameter of a CNT (5, 5) is obtained.