Effect of Chirality and Geometry on the Young’s Modulus of Graphene Structure Using Spring Based Finite Element Approach

The development of nanocomposite materials has led to vast progress in the field of composite materials as well as in finding new solutions to technological problem that have not been solved yet. Among the newly developed materials, the most attracting is the graphene based nanocomposites that has superior mechanical, thermal, optical and electrical properties. The hexagonal structure and the high strength of carbon–carbon bond in graphene yield strong material. Estimation of mechanical properties of the graphene becomes one of the important issues, which should be reasonably and accurately predicted to further promote its application development. Simulation and modeling techniques play a significant role in characterizing mechanical behavior especially for nanomaterials where the experimental measurements are very difficult to conduct. The aim of the current study is to estimate the Young’s modulus of elasticity of single layered graphene sheet using new spring based finite element approach. The use of spring finite elements help to accurately define the interatomic bonded interactions between carbon atoms based on potential energies obtained from molecular dynamics theory. The inclusion of both linear and torsion terms simultaneously has resulted in improved values of the Young’s modulus. The nodes in the finite element model define the position of carbon atoms in the graphene which are connected with appropriate spring-type elements. These elements are used to build the finite element model based on the observation that beam or truss elements require geometrical variables such as area and inertia, which are not required in the case of springs. Each node of this element provides six degrees of freedom (3 translations and 3 rotations) at which the complex interactions presented in the atomistic level can be considered. Parametric study is performed to investigate the effect of chirality and geometric parameters on the Young’s modulus of single graphene layer. The results are in good agreement with the published numerical and experimental results. The obtained results show an isotropic behavior, in contrast to limited molecular dynamic simulations. Young’s modulus of graphene shows a high dependency of stiffness on layer thickness.