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.
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