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Due to their accuracy and reliability, atomistic-based methods such as molecular dynamics (MD) simulations have played an essential role in the field of predictive modeling of single layered graphene sheets (SLGSs(. However, due to the computational costs, applications of these methods are limited to small systems. Additionally, according to the discrete nature of SLGSs, conventional continuum-based methods cannot be utilized to study the mechanical characteristics of them. To overcome these issues, here, a new Atomic-scale Finite Element Method (AFEM) based on the Tersoff-Brenner potential has been developed. Efficiency of the proposed method is evaluated through a numerical example analyzed by both of the proposed method and MD simulation. The results show that the computational cost is much reduced (~100 times), while the accuracy of MD simulation is kept. Furthermore, the effects of initial C-C bond length and number of atoms on the speed of the proposed method is investigated. To mimic the MD simulation completely, periodic boundary conditions have been implemented in the extended AFEM. It is demonstrated that there is a noticeable deviation from MD results without considering this type of boundary conditions.

Keywords: Graphene, Atomic scale finite element method (AFEM), Molecular dynamics simulation, Periodic boundary conditions, Mechanical behavior

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