Comparing different multibody reactive potentials for the elastic properties and nonlinear mechanics of the carbon nanostructures

Abstract

A multiscale model in conjunction with the finite element method is employed to investigate the accuracy of the different reactive empirical bond order potentials involving material and geometric nonlinearities. The four different sets of empirical parameters for the Tersoff-Brenner potential are considered in the present study and among these four sets of empirical parameters, one set is newly proposed herein and three are taken from the available reference sources. The atomistic-continuum coupling is established using kinematics of quadratic type Cauchy-Born rule for establishing the energy density of the unit cell. The finite element method is used to solve the governing equations at the continuum scale. The revised set of empirical parameters is found better for predicting the elastic properties and bond length than the formerly proposed three sets of empirical parameters when compared to those reported using quantum mechanics calculations. The results of the newly proposed potential are compared with DFT based continuum models for a wide range of numerical problems. The proposed potential parameters are tested for a variety of problems such as the energy of the carbon nanotubes with different radii, torsion of the carbon nanotubes, free vibrations of the graphene sheets and carbon nanotubes and numerical simulations of the nanoindentation experiments for circular graphene sheets.