▎ 摘　　要

The elastic properties of graphene sheet at finite strain and curvature tensors are studied employing atomistic-continuum multiscale modelling approach in Lagrangian framework. The strain energy density function at continuum level is expressed as total interatomic potential per unit area of a unit cell incorporating continuum deformation through Cauchy-Born rule. Two different multibody interatomic potentials namely Tersoff-Brenner potential and second generation REBO potential are used to model the interactions between carbon atoms. The in-plane tangent extensional stiffness, bending stiffness, bending-stretching coupling stiffness matrices are obtained by differentiating the strain energy density function. The effect of different combinations of induced strain/curvature on stiffness coefficients is studied for graphene sheet with zigzag, armchair and chiral configurations. It is found that the graphene sheet possesses a material softening behaviour at finite strains and hardening behaviour at finite curvatures. The nonzero normal-shear coupling and tangent bending-stretching coupling stiffness coefficients are reported at finite strain/curvature for the first time in this work. (C) 2014 Elsevier Ltd. All rights reserved.