%0 Generic %1 mokhalingam2019comparing %A Mokhalingam, Aningi %A Ghaffari, Reza %A Sauer, Roger A. %A Gupta, Shakti S. %D 2019 %K graphene %T Comparing quantum, molecular and continuum models for graphene at large deformations %U http://arxiv.org/abs/1908.05090 %X In this paper, the validity and accuracy of three interatomic potentials, commonly used to study carbon nanostructures in molecular dynamics, and the continuum shell model of Ghaffari and Sauer 1 are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) near zero Kelvin 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. For the comparison, the nonlinear response of a square graphene sheet under uniaxial stretching, biaxial stretching and pure bending is studied. Results from the continuum model are in good agreement with those of DFT. The results from the MM3 potential agree well with the DFT results up to the instability point, whereas those from the REBO+LJ and Tersoff potentials agree with the DFT results only within the range of small deformations. In contrast to the other potentials, the Tersoff potential yields 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 obtained from these two approaches agree within an accuracy of about 95%.

@misc{mokhalingam2019comparing, abstract = {In this paper, the validity and accuracy of three interatomic potentials, commonly used to study carbon nanostructures in molecular dynamics, and the continuum shell model of Ghaffari and Sauer [1] are investigated. The mechanical behavior of single-layered graphene sheets (SLGSs) near zero Kelvin 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. For the comparison, the nonlinear response of a square graphene sheet under uniaxial stretching, biaxial stretching and pure bending is studied. Results from the continuum model are in good agreement with those of DFT. The results from the MM3 potential agree well with the DFT results up to the instability point, whereas those from the REBO+LJ and Tersoff potentials agree with the DFT results only within the range of small deformations. In contrast to the other potentials, the Tersoff potential yields 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 obtained from these two approaches agree within an accuracy of about 95%.}, added-at = {2019-09-26T14:48:09.000+0200}, author = {Mokhalingam, Aningi and Ghaffari, Reza and Sauer, Roger A. and Gupta, Shakti S.}, biburl = {https://www.bibsonomy.org/bibtex/2e5a3d8bdc5a48d96c112edf5e6ec94f0/cmcneile}, description = {Comparing quantum, molecular and continuum models for graphene at large deformations}, interhash = {44acbac711f50bcea8b839dc7856ebbf}, intrahash = {e5a3d8bdc5a48d96c112edf5e6ec94f0}, keywords = {graphene}, note = {cite arxiv:1908.05090}, timestamp = {2019-09-26T14:48:09.000+0200}, title = {Comparing quantum, molecular and continuum models for graphene at large deformations}, url = {http://arxiv.org/abs/1908.05090}, year = 2019 }