Effective elastic mechanical properties of single layer graphene sheets

Abstract

The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.

Structure of graphene and its disorders: a review

“…where and L are the thickness and width of a graphene thin film respectively, and is the Poisson’s ratio which is predicted to be 0.1–0.3 for monolayer graphene [199,200]. However, the relation needs to be revised slightly when in-plane shear dominates the applied stress [198]: …”

Molecular Dynamics of Cellulose Amphiphilicity at the Graphene–Water Interface

“…24 The orientation  of the C6 hydroxymethyl groups plays an important role in the stability of cellulose due its control of the type of hydrogen bond formed. 45 During the MD simulations of GC100, these groups remain principally although not exclusively in their initial crystallographic tg orientations (Figure 8a). The tg orientation allows the formation of an intramolecular hydrogen bond in the same chain and intermolecular hydrogen bond with adjacent chains.…”

Vibration and Elastic Buckling Analyses of Singlewalled Carbon Nanocones

“…It is noteworthy that transient dynamics analyses can be performed by using Newmark method due to the advantages of consistent mass matrix which does not yield singularity in numerical integrations. On the other hand, Scarpa and Adhikari [34,35] proposed a beam model considering the shear deformation effects and they found the C-C bond thickness d , Poisson's ratio ν, Young's modulus E and shear modulus G by using the AMBER force model constants [19]. Both of the models in Li and Chou [19] and Scarpa and Adhikari [34] yield the same deformation results as the structural mechanics stiffness constants in the AMBER force model are equal [33] if the corresponding element properties are used given in Table 1.…”

“…Lee and Lee [28] used Timoshenko beam element formulations which include shear deformation effects but they employed Euler-Bernoulli beam element constants (i.e., see Table 1) [23]; this assumption affects the natural frequencies of SWCNC that are found to be lower than those of Euler-Bernoulli beam elements. If shear deformation effects are considered, parameters of shear beam formulations given in Scarpa and Adhikari [34,35] should be used.…”