Young's modulus of graphene based on finite displacement theory

Young's modulus of monolayer graphene with mxn carbon-circles is considered based on least-energy principle (LEP) and finite displacement theory (FDT). The relationships between the Young's modulus and the numbers of carbon-circles of graphene are obtained. The results suggest that the Young's modulus of graphene increases with the increasing number of carbon-circles in y-direction, but reduces with the increasing number in x-direction, and gradually comes to the constant 0.289k/d.