MODELLING OF DEFORMATION PROCESSES OF CARBON NANOTUBES

The article presents the results of the calculations of the modelling task in the framework of the continuum model done with the help of the finite-element method. The modelling task dealt with the incurvature of single- and multiwalled carbon nanotubes at variation of their length and thickness. It is shown for the first time that the nonlinear dependence of stiffness on carbon nanotubes diameter and length at the nanometric scale corresponds to the contemporary views of the macroscopic theory of continuum mechanics. The comparison of the calculation results and literature experimental data shows that the lyotropic mesomorphic state appears in the carbon nanotubes dispersions at the aspect ratio (length/diameter of nanotubes) much bigger than in thermotropic calamitic nematogenes and lyotropic organic nematics. From the theoretical point of view, the results of the present research expand the boundaries of applicability of the continuum mechanics theory from macro- to nanoscale. From the practical point of view, the results of the calculations of the dependence of stiffness on aspect ratio will help to define the boundaries of usage of carbon nanotubes of various structure as hotropic mesogenes, as abrasive materials and as lubricant fillers.