Abstract
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) at the nanoscale. However, their applications are limited due to the computational costs. Additionally, consistent with the discrete nature of SLGSs, conventional continuum-based methods cannot be utilized to study the mechanical characteristics of these nanostructures. To overcome these issues, a new Atomic-scale Finite Element Method (AFEM) based on the Tersoff-Brenner potential has been developed in this study. Efficiency of the proposed method is demonstrated employing several numerical examples and its applicability is carefully testified in the case of perfect and defected SLGSs. To facilitate a better comparison, the mechanical behavior obtained by this method is compared with the one determined via MD simulation in various case studies. The results reveal that the proposed method has the accuracy of MD simulations and the speed of continuum-based approaches, simultaneously.
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