Prediction of nonlocal scale parameter for carbon nanotubes

Abstract

Based on the theory of nonlocal elasticity, a nonlocal shell model accounting for the small scale effect is developed for the bending characteristics of CNTs subjected to the concentrated load. With this nonlocal shell model, explicit expressions are derived for the bending solutions. To extract the proper values of nonlocal scale parameter, we have made molecular dynamics (MD) simulations for various radii and lengths of armchair and zigzag CNTs, the results of which are matched with those of nonlocal continuum model. It is found that the present nonlocal elastic shell model with its appropriate values of nonlocal scale parameter has the capability to predict the bending behavior of CNTs, which is comparable with the results of MD simulations. Moreover, exact closed form solutions for the nonlocal scale parameter for zigzag and armchair CNTs are obtained. The results show that nonlocal scale parameter is independent of the length of CNTs, and dependent on the radius of CNTs.