Refined multiscale model based on the second generation interatomic potential for the mechanics of graphene sheets

摘要

Computationally efficient multiscale model based on the refined constitutive law, including second generation reactive empirical bond order potential with dihedral energy term, is employed to investigate the static response of the graphene sheets under transverse and in-plane compressive loads including material nonlinearity through atomic interactions and Green-Lagrange geometric nonlinearity through the strain displacement relations. The bending modulus of the graphene sheet predicted without considering the dihedral energy term in the constitutive law is almost half than those of predicted through first principle calculations. The inclusion of the dihedral energy term predicts bending modulus close to those of through first principle calculations. The atomistic and continuum deformations are coupled through the Cauchy-Bom rule. In the present study, the effect of the dihedral energy term on the linear and nonlinear bending and postbuckling response of the graphene sheets under transverse and in-plane compressive loads is investigated in detail. The governing finite element equations for the graphene sheet are derived through the principle of minimum potential energy. The spatial approximation of the graphene sheet at the continuum scale is attained through the finite element method.