Equilibrium configuration and continuum elastic properties of finite sized graphene

This paper presents a continuum mechanics approach to modelling the elastic deformation of finite graphene sheets based on Brenner's potential. The potential energy of the graphene sheet is minimized for determining the equilibrium configuration. The four edges of the initially rectangular graphene sheet become curved at the equilibrium configuration. The curving of the sides is attributed to smaller coordination number for the atoms at the edges compared to that of the interior atoms. Considering two graphene models, with only two or all four edges constrained to be straight, the continuum Young's moduli of graphene are computed applying the Cauchy–Born rule. The computed elastic constants of the graphene sheet are found to conform to orthotropic material behaviour. The computed constants differ considerably depending on whether a minimized or unminimized configuration is used for computation.