Coupled molecular/continuum mechanical modeling of graphene sheets

Single layer graphene sheets (SLGSs) are studied by using the coupling of atomistic and continuum domains based on least squares projections of atomistic and continuum displacement fields. The augmented problem is solved by using the Lagrange multiplier method and it allows multiple numbers of molecular mechanic (MM) domains in a single continuum mechanic (CM) domain in which the MM domain(s) can be placed arbitrarily. In the atomistic models, harmonic and modified Morse potentials are employed to solve sample problems. In order to verify the proposed approach, local deformation and damage of SLGSs are examined by solving sample static benchmark and fracture mechanic problems; then, comparisons are made with the results reported in literature. The proposed approach can compute the deformations of SLGSs in high accuracy, is very flexible to compute local solutions and can easily be applied to other materials.