A nonlinear molecular mechanics model for graphene subjected to large in-plane deformations

In this paper we present a fully nonlinear stick-and-spring model for graphene subjected to in-plane deformations. The constitutive behaviors of sticks and springs are defined, respectively, by the modified Morse potential and a nonlinear bond angle potential. The equilibrium equations of the representative cell are written considering large displacements of the nodes (atoms) and the stability of the solutions is assessed using an energy criterion. The solutions for the uniaxial load cases along armchair and zigzag directions show that graphene is isotropic for small deformations, while it exhibits anisotropy when subjected to large deformations. Moreover, graphene shows a negative Poisson's ratio after a critical value of deformation. In the case of equibiaxial load, multiple solutions of the equilibrium are found and graphene can experience asymmetric deformations despite the symmetry of the external loads. The nonlinear formulation of the equilibrium is then linearized by introducing the hypothesis of small displacements. The expressions of Young's modulus and Poisson's ratio are derived.