A Research Of Cantilever Carbon Nanotube Subjected Pure Bending Moment

Since their discovery in1991, carbon nanotubes’(CNTs) outstanding performance andbroad potential application have aroused widespread concern. And the mechanical behaviorof CNT has become one of the international hot issues.There are a lot of research on the mechanical properties of CNTs so far. Due to thedifficulty of the experimental method on the mechanical properties of CNTs, investigating themechanical properties of CNTs is mainly from the theoretical method, including moleculardynamics simulations and continuum model. When using molecular dynamics simulationsforthe large size of the atomic system, because of the large atomic number, long time span, andhigh cost of computing, its practical applications has been largely restricted. Therefore,seeking high-efficiency, high-precision analysis is an important issue in the field ofnanomechanics.Continuum mechanics is a relatively well developed subject, based on thesimilarity of nano-structure and macro-structure, the basic theory of continuum mechanics isa very effective method for analysis of the mechanical properties of CNTs.Nonlocal elastic shell model based on the semi-moment theory is developed and appliedto investigate the small scale effect on the pure bending problem of the cantilever carbonnanotube (CNT). Analytical expressions of the stress are derived for the nonlocal elasticbending problem.Molecular dynamics simulation has been taken for the pure bending of CNTs. the resultsobtained from molecular dynamics simulation are in good agreement with those obtainedfrom the semi-moment theory.The simulation resultshave shown the results obtain fromsemi-moment theory ismore accurate on larger diameter for the same length of CNTs. Smalldiameter carbon nanotubes in large loads will lead to the failure of solution of thesemi-moment theory. Further studies showed that semi-moment theory will cause large errorsfor the slender and stubby CNTs, and the semi-moment theory is only valid for specific rangeof the aspect ratio CNTs.At last, based on the results of the previous researches, nonlocal elastic shell modelbased on the semi-moment theory is developed and applied to investigate the small scaleeffect on mechanical properties of single walled carbon nanotubes. The small-scale effect is taken into account and is incorporated in the formulation of the equilibrium equations and thedeformation compatibility equation. And the internal force and displacement field theoreticalsolution are derived for the nonlocal elasticity. The results show that the CNTs with relativelysmall size have obvious scale effect, the scale effect is dependent on the CNT radius and thescale factor. Scale effect is more obvious when the CNT radius is smaller. With the radius ofthe CNT increasing the scale effect gradually reduces. When the CNT radius reaches a criticalvalue, the scale effect can be ignored, and the classical continuum mechanics is valid.