Application of gradient elasticity to armchair carbon nanotubes: Size effects and constitutive parameters assessment

The central focus of the paper is set on modelling of bending of armchair carbon nanotubes by means of the gradient elasticity theory. Influence of small-size effects on the Young's modulus is investigated. An attempt to determine small size (or nonlocal) parameter employed in the Bernoulli-Euler and Timoshenko gradient formulations is presented. To obtain such a goal, the paper provides an extensive set of molecular structural mechanics simulations of armchair nanotubes with different loading and kinematic boundary conditions. Dependence of the Young's modulus on small size effects is clearly noticed. Based on these results, small scale parameters for the gradient model are identified and limits of the method are pointed out. Results of the study indicate that the widely used theory should be modified to obtain a physically justified and reliable nanobeam model based on Bernoulli-Euler or Timoshenko kinematic assumptions.