Stability, Elastic Properties, And Contact Problems Of Carbon Nanotubes

Most theoretical investigations on the mechanical properties of carbon nanotubes (CNT) are based on atomic theories, which are not suitable for the large-scale simulation. On the contrary, continuum mechanics and finite element (FE) method have been proved to be promising tools to deal with the multi-scale computations. In this paper, the configuration stability, the elastic properties and the contact problems of CNT are studied by the continuum mechanics and FE. The applicability of macro-scale mechanics in nano-scale is also discussed. Firstly, the criteria determining the minimum radii of CNT are deduced by introducing the surface energy factor into the boundary conditions of CNT. The minimum radii deduced based on cylindrical column model and cylindrical shell model are similar to those obtained by the experiments and the modeling via quantum mechanics. Secondly, based on the membrane model and exponential Cauchy-Born rule, the constitutive equations of single wall carbon nanotube (SWCNT) are deduced by qusi-continuum method. Young's modulii and Poisson's ratio obtained are within the range of the results from the experiments and other theoretical researches. Also, the influences of the structure on the elastic properties of SWCNT are studied. Finally, FE software ABAQUS is used to model the contact of SWCNTs. The elastic constants are obtained from the deduction before and van der Waals interaction is defined by user subroutine UINTER.