Monte Carlo-Based Finite Element Method for the Study of Randomly Distributed Vacancy Defects in Graphene Sheets

Liu Chu,Hongliang Xiang,Eduardo Souza De Cursi,Yazhou Qin,Xunqian Xu,Jiajia Shi

doi:10.1155/2018/3037063

Abstract

This paper proposed an effective stochastic finite element method for the study of randomly distributed vacancy defects in graphene sheets. The honeycomb lattice of graphene is represented by beam finite elements. The simulation results of the pristine graphene are in accordance with literatures. The randomly dispersed vacancies are propagated and performed in graphene by integrating Monte Carlo simulation (MCS) with the beam finite element model (FEM). The results present that the natural frequencies of different vibration modes decrease with the augment of the vacancy defect amount. When the vacancy defect reaches 5%, the regularity and geometrical symmetry of displacement and rotation in vibration behavior are obviously damaged. In addition, with the raise of vacancy defects, the random dispersion position of vacancy defects increases the variance in natural frequencies. The probability density distributions of natural frequencies are close to the Gaussian and Weibull distributions.

Highlights

Graphene, discovered in 2004 [1], is a two-dimensional (2D) carbon nanomaterial composed of a hexagonal honeycomb lattice
With the purpose of combining the Monte Carlo simulation (MCS) with the beam finite element model (FEM), the flowchart of Monte Carlo-based finite element model (MC-FEM) is described in Figure 2, which is summed up in the 7 steps: (1) The original configuration of graphene lattice is defined, including the geometrical characteristic corresponding parameters of the bonds in the honeycomb microstructure, as well as the thickness or diameter of the cross section in the beam FEM
The precision of material parameters strongly influences the results of the finite element model of graphene sheets

Summary

Introduction

Graphene, discovered in 2004 [1], is a two-dimensional (2D) carbon nanomaterial composed of a hexagonal honeycomb lattice. Graphene has an atomic-scale honeycomb lattice consisting of carbon atoms and sp hybrid orbitals. Size-dependent continuum theories are the other promising methods [20,21,22,23,24], which consist of the nonlocal elasticity theory [20], strain gradient theory [21,22,23], and modified couple stress theory [24]. Atomistic-based methods are expensive for systems with large amounts of atoms, while classical size-dependent methods face difficulties on analyzing the vacancy defects with random distributions

Methods

Results

Conclusion