Hyperelastic tension of graphene

In this paper, we investigate the hyperelastic tensile behaviour of single layer graphene sheets (SLGSs). A one-term incompressible Ogden-type hyperelastic model is chosen to describe the mechanical response of C-C bonds. By establishing equality between the Ogden strain-energy and the variation of the Tersoff-Brenner interatomic potential, three different geometries of SLGSs are studied under tensile loading. We compute the Young's modulus, the finite-deformation Poisson's ratio, ultimate strains, total reactions, and the variation of the potential energy per carbon atom for large strains. Numerical simulations are compared with results obtained by molecular mechanics and molecular dynamics simulations, finite elements, continuum mechanics theory, and experiments. Our predictions are validated, revealing the potential predictive capabilities of the present hyperelastic framework for the analysis of graphene in the context of infinitesimal and large deformations. The good agreement found between our calculations and the published data suggests that graphene may be described as a hyperelastic material.