A Reduced-Order General Continuum Method for Dynamic Simulations of Carbon Nanotube

Abstract

A reduced-order general continuum method for simulating three dimensional transient mechanical behaviors of carbon nanotube is presented. The method builds the potential energy density for carbon nanotubes by applying the macroscopic deformation gradient to the atomistic energy potential based on the modied nite element degrees of freedom could be much less than the actual atomic degrees of freedom; (2) reduced modeling error due to the application of the same atomistic energy potential as that is used in molecular dynamic method; (3) the explicit time integration schemes allow for e- cient simulation especially for highly nonlinear carbon nanotube deformations. The article starts with a review on the development of reduced order numerical methods for carbon nanotube, then follows the introduction and implementation details of the method. Finally a series of numerical experiments are presented including two dimensional carbon atomic ring interacting with carbon substrate, static deformations such as elongation, buckling, and twisting of carbon nanotube, and dynamic deformations of CNT-AFM probe.