A Kriging Surrogate Model for Uncertainty Analysis of Graphene Based on a Finite Element Method.

Jiajia Shi,Liu Chu,Robin Braun

doi:10.3390/ijms20092355

Abstract

Due to the inevitable presence of random defects, unpredictable grain boundaries in macroscopic samples, stress concentration at clamping points, and unknown load distribution in the investigation of graphene sheets, uncertainties are crucial and challenging issues that require more exploration. The application of the Kriging surrogate model in vibration analysis of graphene sheets is proposed in this study. The Latin hypercube sampling method effectively propagates the uncertainties in geometrical and material properties of the finite element model. The accuracy and convergence of the Kriging surrogate model are confirmed by a comparison with the reported references. The uncertainty analysis for both Zigzag and Armchair graphene sheets are compared and discussed.

Highlights

With a two-dimensional (2D) honeycomb lattice, graphene can be wrapped up into zero-dimensional (0D) fullerenes, rolled into one-dimensional (1D) nanotubes, or stacked into three dimesnional (3D) graphite [1]
This paper proposes the application of the Kriging surrogate model (KSM) to represent the uncertain and complicated relationship between the elastic response of graphene sheets and the external forces
In the first order natural frequency, the prediction results of KSM is larger than the results of Liu [38], Kudin [39], and Wei [40]

Summary

Introduction

With a two-dimensional (2D) honeycomb lattice, graphene can be wrapped up into zero-dimensional (0D) fullerenes, rolled into one-dimensional (1D) nanotubes, or stacked into three dimesnional (3D) graphite [1]. The unexpected mechanical properties of graphene are experimentally verified through nano-indentation by the atomic force microscope (AFM) [8]. On the aspects of experimental measurements, the in-plane Young’s modulus of bulk graphite [9] is in the range of 1.02 ± 0.03 TPa. In the tensile test [10], a broad range of stiffness values (0.27 TPa to 1.47 TPa) were obtained, with breaking strengths ranging from 3.6 to 63 GPa. In addition, the defects in the graphene contribute to the deviation in the bending rigidity in the test results of suspended monolayer graphene membranes [11]. The Young’s modulus is extracted as 0.5 TPa [12] in the measurement of the bending stiffness of graphene sheets by AFM nano-indentation. The Young’s modulus equals 1.0 ± 0.1 TPa and the corresponding intrinsic stress is 130 ± 10 GPa at a strain of 0.25 [8]

Results

Discussion

Conclusion