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

Abstract

In this paper, a reduced-order general continuum method for simulating the three-dimensional transient mechanical behaviors of carbon nanotube (CNT) 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 a modified Cauchy-Born rule. The minimum energy principle in finite element methods can be used to obtain the equilibrium solution of the resulting equations. To compute the dynamic behaviors of carbon nanotubes, an explicit Newmark time integration scheme is applied to augment the static formulation. Details of the proposed formulation to study CNT dynamics are described. The results of simulation cases are then presented. The cases include a two-dimensional carbon atomic ring interacting with carbon substrate, static deformation of carbon nanotube, such as elongation, buckling, and twisting, and dynamic deformation of CNT-AFM probe with point force loading. Where possible, the results are compared with those obtained by molecular dynamics and atomic based finite element methods. The comparison shows that the current method can capture unique nonlinear characteristics of CNTs and provide predictions of the CNT’s transient behaviors.