FE2${\mathrm{FE}}^{2}$ method to model graphene subjected to in‐plane loading

Abstract This paper investigates the mechanical properties of carbon‐based nanostructures, in particular graphene, using the method. The local boundary value problem is calculated using molecular mechanics and is therefore, in contrast to continuum mechanics, discrete. In the case of graphene as a microstructure, atomistic interactions occur with a range of up to three or more atoms. For the local boundary value problem, a representative volume element is developed that is compatible with the atomistic interactions. Boundary effects resulting from the molecular mechanical consideration are eliminated. Boundary conditions compatible with the Hill–Mandel condition are formulated for the local boundary value problem. The results are verified with fully atomistic simulations.