Modelling of a single layer graphene membrane

Abstract: The present contribution deals with the modeling of thin graphene membranes. Such membranes have a significant electrical and physical properties used for nano or micro devices like resonators and Atomic Force/mass Measurements (AFM) [1]. The membrane is considered as a homogenized graphene monolayer on the macroscopic structural scale. In this development the stress response on the scale of the actual atomistic microstructure is resolved based on the CBN rule for the inter-atomic kinematics. Explicit expressions for the homogenized membrane forces are derived, assuming atomistic pairwise interaction between the atoms at zero degrees Kelvin, as well as the resulting effective membrane stiffness. The resulting static behavior, using the proposed modeling approach, of a graphene monolayer sheet is presented and compared with an experimental AFM. Subsequently, a proposed potential based on Tersoff Brenner formulation is used for the multiscale modeling, where the standard parameters generally shows a too week stiffness response of TB based method. Consequently, in order to ameliorate the result, a fine tuning of the TB-parameters is proposed by comparing lattice responses of different quantum mechanical simulations is considered.