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

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\%.

Atomistically-informed continuum modeling and isogeometric analysis of 2D materials over holey substrates

“…The agreement between continuum and MS modeling hinges crucially on geometric nonlinearity in the Kirchhoff-Love shell model. However, we find that material nonlinearity in the stress-strain model is of lesser significance, and the aforementioned continuum-MS agreement is obtained using only a simple linear isotropic St. Venant-Kirchhoff model, in contrast to more elaborate 2D material models like those of [15][16][17] for graphene.…”

“…Sauer and collaborators have previously pursued similar objectives with a focus on graphene. In particular, they have proposed to use isogeometric analysis (IGA) [10,11] of Kirchhoff-Love shell theory [12][13][14] in this context, developing and calibrating specialized constitutive models [15][16][17] and simulating vdW interactions with substrates through a Lennard-Jones (LJ) [18] potential [19,20]. We follow a broadly similar approach of using IGA of Kirchhoff-Love shells to simulate 2D materials, but introduce the following novel contributions:…”

Electric current distribution induced by applied magnetic field in a bent graphene nanoribbon cantilever

“…The interaction energy between the carbon atoms is described by the Tersoff potential [39,40], and the initial velocities are zero. The Tersoff potential is one of the empirical interatomic potentials, and comparative studies of simulation results with empirical interatomic potentials and experiments have been reported [41,42].…”

Review on Carbon Nanomaterials-Based Nano-Mass and Nano-Force Sensors by Theoretical Analysis of Vibration Behavior

“…With this approach, Li and Chou calculated Young’s moduli and shear moduli of GSs and SWCNTs with different diameters, which were 0.85~1.05 TPa and 0.2~0.5 TPa, respectively, as shown in Figure 3 . Up to now, the approach of MSM has been widely adopted for calculating the material properties (e.g., Young’s modulus and shear modulus) of CNTs (e.g., [ 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 ]) and GSs (e.g., [ 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 , 115 , 116 ]) for mechanical analysis with continuum shell and beam models.…”