Comparing quantum, molecular and continuum models for graphene at large deformations

In this paper, the validity and accuracy of three interatomic potentials and the continuum shell model of Ghaffari and Sauer [1] are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) under uniaxial stretching, biaxial stretching and pure bending is studied for this comparison. The validity of the molecular and continuum models is assessed by direct comparison with density functional theory (DFT) data available in the literature. The molecular simulations are carried out employing the MM3, Tersoff and REBO+LJ potentials. The continuum formulation uses an anisotropic hyperelastic material model in the framework of the geometrically exact Kirchhoff-Love shell theory and isogeometric finite elements. Results from the continuum model are in good agreement with those from DFT. The results from the MM3 potential agree well up to the point of material instability, whereas those from the REBO+LJ and Tersoff potentials agree only for small deformations. Only the Tersoff potential is found to yield auxetic response in SLGSs under uniaxial stretch. Additionally, the transverse vibration frequencies of a pre-stretched graphene sheet and a carbon nanocone are obtained using the continuum model and molecular simulations with the MM3 potential. The variations of the frequencies from these approaches agree within an error of 5%.