Structural deformations of two-dimensional planar structures under uniaxial strain: the case of graphene

In the present work, a method for the study of the structural deformations of two dimensional planar structures under uniaxial strain is presented. The method is based on molecular mechanics using the original stick and spiral model and a modified one which includes second nearest neighbor interactions for bond stretching. As we show, the method allows an accurate prediction of the structural deformations of any two dimensional planar structure as a function of strain, along any strain direction in the elastic regime, if structural deformations are known along specific strain directions, which are used to calculate the stick and spiral model parameters. Our method can be generalized including other strain conditions and not only uniaxial strain. We apply this method to graphene and we test its validity, using results obtained from ab initio density functional theory calculations. What we find is that the original stick and spiral model is not appropriate to describe accurately the structural deformations of graphene in the elastic regime. However, the introduction of second nearest neighbor interactions provides a very accurate description.