Molecular and Continuum Mechanics Modeling of Graphene Deformation

The elastic response of a circular single graphene sheet with a diameter of 65.32 Å under a transverse central load is studied using molecular dynamics (MD), closed-form elasticity solution (EL), and finite element method (FEM). Results showed that the mismatch in deformation profiles between MD calculations and continuum mechanics methods is about 8~9% at a central deflection of one graphene layer thickness. The mismatch reduces to less than 5% when the central deflection increased to a 10-layer thickness. The mismatch rooted from mechanics: MD predicts predominant bond stretching mode while continuum mechanics predict a bending to stretching transition process under increasing deflection. Results suggest that continuum mechanics can yield predictions close to molecular mechanics under large deformation for certain loading configurations when modes of deformation are similar.