Abstract
The stochastic distributed placement of vacancy defects has evident effects on graphene mechanical property, which is a crucial and challenged issue in the field of nanomaterial. Different from the molecular dynamic theory and continuum mechanics theory, the Monte Carlo based finite element method (MC-FEM) was proposed and performed to simulate vibration behavior of vacancy defected graphene. Based on the Monte Carlo simulation, the difficulties in random distributed location of vacancy defects were well overcome. The beam element was chosen to represent the exact atomic lattice of the graphene. The results of MC-FEM have a satisfied agreement with that in the reported references. The natural frequencies in the certain vibration mode were captured to observe the mechanical property of vacancy defected graphene sheets. The discussion about the parameters corresponding with geometry and material property was accomplished by probability theory and mathematical statistics.
Highlights
For the parameters corresponding to material properties of defect-free graphene monolayer, Young’s modulus and intrinsic strength are 1.0 TPa and 130 GPa [1]
Some size dependent non-classical continuum theories have been studied in the research field of graphene sheets, which includes the strain gradient theory [13], modified couple stress theory [14], and nonlocal elasticity theory [15]
According to the overview of the existing literature, it can be found that the influence of the vacancy defects on the mechanical behavior of nanostructures has been studied in very few papers
Summary
For the parameters corresponding to material properties of defect-free graphene monolayer, Young’s modulus and intrinsic strength are 1.0 TPa and 130 GPa [1]. The motivation of this study is to effectively analyze vibration behavior of defected graphene sheets when the vacancy defects are randomly distributed. Since the physical experiments of vacancy defected graphene sheets are difficult and expensive, numerical simulation methods are another promising supplement that need to be developed. Combining the Monte Carlo simulation with the finite element method to effectively simulate the random dispersed vacancy defects in graphene sheets is a perspective and feasible method. The Monte Carlo simulation as a sophisticated sampling method has been widely applied in the research of phase transition and magnetism of graphene sheets [20,21,22,23]. The discussion extensively consists of the effect of amount of vacancy defects and geometrical and material parameters in the natural frequencies of vacancy defected graphene sheets.
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