Young's modulus of graphene based on variation principle and energy conservation

Tensile strain in x-direction for monolayer graphene with m x n carbon-circles is considered based on variation principle and energy conservation. The relations between the Young's modulus in x-direction and the number of carbon-circles of graphene are obtained. The results show that the Young's modulus of graphene in x-direction is independent of the number of carbon-circles in x-direction, but it increases with the increasing number of carbon-circles in y-direction and finally comes to the constant(8 root 3k(theta))/(r(0)(2)d).