Size effect in single layer graphene sheets and transition from molecular mechanics to continuum theory

The size-dependent mechanical response of graphene is investigated with an entirely nonlinear molecular mechanics approach. Finite element (FE) simulations under uniaxial and equibiaxial tensile loads are carried out on graphene sheets with increasing size. It is found that the response of graphene remains unchanged after a threshold size. Furthermore, anisotropy is observed for large deformations and a negative Poisson's ratio is found after a critical strain for the zigzag uniaxial load case. The threshold size defines the transition to the continuum theory, which is developed as a membrane model in the fully nonlinear context of finite elasticity. The constitutive parameters of the model are calibrated by fitting the results of the FE simulations. The proposed model represents the basis for accurate predictions of the response of graphene subjected to large in-plane deformations. Nonlinear laws for the size-dependent elastic properties of graphene are derived. These laws can be used in linear elasticity-based models to take into account for material nonlinearity, anisotropy and size effect. Finally, a sensitivity analysis of the molecular mechanics model to the parameters of the interatomic potentials is carried out. The discussion of the results gives insights into the influence of each parameter and useful remarks for the molecular mechanics modeling of graphene.