Molecular Dynamics Simulation Of Effective Elastic Properties And Buckling Behvior Of Carbon Nanotubes

The unique physical properties and many kinds of configurations of carbon element have been gradually discovered, understood and used. The development of our society has been greatly accelerated by the application of graphite electrodes, the exploration of composites based on carbon fibre, diamond films, etc. Theoretical predictions and numerous experiments have shown high strength, rigidity and toughness as well as special electrical properties for carbon nanotubes (CNTs) since they were first reported. Nanotubes are considered to be the most promising materials of applications in nano- engineering and nano-composites, which requires a clear understanding of the mechanical properties and deformation mechanism of CNTs.In this paper, the molecular dynamics (MD) method is used to investigate the mechanical properties of carbon nanotubes. In the MD simulations, the nanotube is considered as a congeries of individual atoms, the movement equations are established for every atom, and the deformation behavior of nanotubes can be determined by the trajectories of each atom. Thus, the dynamics process in realistic environments is re-presented with MD methods. Due to the microscopic understanding of deformation mechanism and intrinsic description of characteristics of a structure, the MD method plays an important role in the study on the mechanical behavior of CNTs.This paper deals with the deformation and buckling behavior of carbon nanotubes under mechanical loads by using MD methods. The simple loads considered are axial compression, torsion and external pressure, and the combined loads involve simultaneous actions of axial compression and external pressure, axial compression and torsion, as well as axial compression and thermal load. The MD method is used to determine the postbuckling equilibrium paths, the variation of energies with stain and the typical buckling modes. In these studies we focus on the effect of temperature variation on the bucking and postbuckling behavior of nanotubes. Simulations results also show the buckling loads are strongly size dependent. Based on a comparison of computational results with the higher order shear deformation shell theory, the effective elastic properties of single- and double-walled carbon nanotubes (SWCNTs and DWCNTs) s are determined.For the buckling of SWCNTs under simple loads, the atomic interactions and strain energies in both states of before and after the critical point are monitored and recorded during the MD simulations. Three typical buckling modes under different loads are presented. According to comprehensive numerical results, differences of buckling and postbuckling properties under axial compression, torsion and radial pressure are investigated in detail. MD results reveal the buckling behavior of SWCNTs depends strongly on the temperature, while the effect of temperature varies with the loading conditions. The results also show that the buckling loads are size dependent. The additional van der Waals forces will affect the postbuckling equilibrium paths in cases of torsion and external pressure, and the effect of van der Waals interactions on the postbuckling behavior of SWCNTs under axial compression can be negligible.For the buckling of SWCNTs under combined loads, the internal force-stain curves and deformation patterns are examined with various values of load-proportional parameter. The mechanical properties under combined loads are compared with those under corresponding pure loads. It is found that the buckling behavior of SWCNTs subjected to combined loads is also strongly size dependent. The interaction buckling curves are obtained for nanotubes under combined loading case of axial compression and external pressure, as well as axial compression and torsion. The effect of temperature on mechanical buckling of SWCNTs under combined axial compression and torsion are significant. Rise in temperature results in decrease of interactive buckling loads and postbukling equilibrium paths. It is worthy to found that, for SWCNTs subjected to simultaneous actions of axial compression and thermal load, strongly atomic oscillation at high temperature leads to large decrease of critical buckling temperature for zigzag tubes with relatively small radius.The simulation results demonstrate that the carbon nanotube has ability to repair large holes in the lattice automatically. The holes are mended and transform to Stone-Wales structure in most cases.In the account of great scatter values of mechanical properties for CNTs, an orthotropic shell model is presented, and the effective elastic properties of SWCNTs and DWCNTs are determined by direct MD buckling measuring combined with the use of higher order shear deformation shell theory. The numerical results show that the Young's modulus decreases as the temperature increases. With the temperature increasing from 100 K to 700 K, the shear modulus increases and exhibits strong temperature dependence. However, at temperature≥700 K, the dependence becomes very weak. When the material properties and effective wall thickness are properly chosen, the results obtained by continuum mechanics agree well with MD results.In the above studies, many numerical results are obtained firstly, and, therefore, we believe that it is of great importance of understanding the mechanical response of carbon nanotubes, and is helpful to accelerate nanotube-based composites and engineering. The present investigations also provide theoretical basis for applications of continuum elastic theory to nano-scale structures.