The study of mechanical properties of graphene by molecular mechanics and equivalent model

• Main Authors: Tse-AnChen, 陳則安
• Other Authors: I-Ling Chang
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/45325921697992582834

碩士 === 國立成功大學 === 機械工程學系碩博士班 === 101 === This research developed molecular mechanics method and energy equivalent model to investigate the elastic properties of graphene as well as to predict its fracture. In molecular mechanics method, a representative unit cell of graphene was considered and only the bond stretching and bending energies were considered assuming that the infinite graphene sheet was under uniform in-plane loading. The deformation of the graphene could be calculated under either the minimum energy or uniform strain assumptions. It was found that the deformation inside the representative unit cell is not uniform at minimum energy condition due to the non-uniform discrete distribution to the atoms. The fracture criteria based on critical bond length was used to predict the fracture strain of graphene. Moreover, the elastic properties were observed to be in-plane isotropic while the fracture strains were directional dependent. The spring and beam elements were employed as replacements for covalent bond between atoms using the energy equivalent concept. Other than single bond equivalence as commonly suggested in the literature, an equivalence based on the representative unit cell was proposed and a modified beam element was suggested. The finite element calculations of the graphene under loading were performed and the results were compared with the one based on molecular mechanics method. It would found that the mechanical properties calculated using modified beam element were in good agreement with molecular mechanics method. The predicted fracture strains of armchair graphene were higher than the zigzag one, which was consistent with the molecular dynamics simulation results reported in the literature. In this research, we successfully implemented the analytical calculation and finite element method to study the mechanical properties of graphene. It was concluded that the beam element proposed in the literature needs to be modified in order to provide correct results. With the modified equivalent element integrating with finite element analysis, we could easily extend the model size to overcome the computational obstacle usually encountered in molecular dynamics. We could effectively and efficiently investigate the size and chirality effects of graphene nanoribbons and carbon nanotubes to benefit the design of nano-devices.