A concurrent multiscale simulation for nonlinear flexural and postbuckling analyses of single-layer graphene sheets at finite temperature

A computationally efficient numerical simulations based on an atomistic-continuum coupling in conjunction with a finite element model are presented for the static response of graphene sheets under transverse and in-plane compressive loads at finite temperatures. The present multiscale approach incorporates the dihedral energy terms in atomic interactions based on Tersoff-Brenner potential and Green-Lagrange nonlinearity through strain displacement relations. The atomic level deformations (bond lengths, bond angles and dihedral angles) are coupled to continuum scale through the quadratic-type Cauchy Born rule. The governing equations at continuum scale are solved through finite element method. The separate subroutine is developed to calculate stress/moments resultants, and the tangent constitutive matrix is embedded in the Gauss-quadrature numerical integration of the elemental equations. The influence of dihedral energy term and finite temperature on the linear and nonlinear bending response and postbuckling analyses of graphene sheets is investigated in detail. In addition, a new set of empirical parameters proposed by authors in their earlier work has also been examined for the nonlinear response of graphene sheets.