Homogenized Elastic Properties of Graphene for Small Deformations

Abstract

In this paper, we provide the quantification of the linear and non-linear elastic mechanical properties of graphene based upon the judicious combination of molecular mechanics simulation results and homogenization methods. We clarify the influence on computed results by the main model features, such as specimen size, chirality of microstructure, the effect of chosen boundary conditions (imposed displacement versus force) and the corresponding plane stress transformation. The proposed approach is capable of explaining the scatter of the results for computed stresses, energy and stiffness and provides the bounds on graphene elastic properties, which are quite important in modeling and simulation of the virtual experiments on graphene-based devices.

Elastic Properties and Stability of Physisorbed Graphene

“…Since then, there have been many atomistic calculations specifically devoted to the elastic properties of graphene [28]. The results depend on the specific microscopic model used (see Table 1) and on the type of boundary conditions applied [17]. When calculations are performed on a finite-size graphene sample, the Young modulus is found to be size dependent: below 3nm, the Young modulus decreases by ∼10% per each nm reduction [55].…”

“…On the one hand, experimental measurements of the elastic response of nanostructures by nanomechanics is still challenging (see Section 5). On the other hand, "virtual experiments" performed on the computer may lead to scattered data owing to the shape, size and boundary conditions applied to the sample [17].…”

Atomistic Modelling of 2D Stress Distribution Around Discontinuities

“…Please note that the hole is only approximately elliptical since the discrete nature of the atomistic system gives jagged edges with unsymmetrical atom bonds. This is the region where the most pronounced discrepancy between the continuum and the atomistic model results is to be expected due to the boundary effects which play a significant role in the graphene properties as shown in [20]. Fig.…”

Mechanical Properties and Eigenfrequencies of Graphene Sheets

“…1 [6], [11]- [12]. The main contributions to the total steric energy come from the first four terms of equation (1). Under the assumption of small deformation, the harmonic approximation is adequate for describing the energy [5].…”

“…Young's modulus, tensile or compressive strength, eigenfrequencies and buckling are investigated by number of researchers. Intensive research is also oriented to the application of nanostructures in electrical and chemical engineering, as well as in biological sciences [1].…”