  We derive analytical expressions for the Young's modulus and the Poisson's
ratio of the graphene nanoribbon, in which free edges are warped by the
compressive edge stress. Our analytical formulas explicitly illustrate the
reduction of the Young's modulus by the warped free edges, leading to the
obvious width dependence for the Young's modulus of the graphene nanoribbon.
The Poisson's ratio is also reduced by the warped free edges, and negative
Poisson's ratio can be achieved in the graphene nanoribbon with an ultra-narrow
width. These results are comparable with previous theoretical works.
