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Research Papers

Numerical Analysis of Circular Graphene Bubbles

[+] Author and Article Information
Rui Huang

e-mail: ruihuang@mail.utexas.edu
Department of Aerospace Engineering and Engineering Mechanics,
University of Texas,
Austin, TX 78712

1Corresponding author.

Manuscript received January 10, 2013; final manuscript received February 27, 2013; accepted manuscript posted April 8, 2013; published online May 31, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 040905 (May 31, 2013) (9 pages) Paper No: JAM-13-1017; doi: 10.1115/1.4024169 History: Received January 10, 2013; Revised February 27, 2013; Accepted April 08, 2013

Pressurized graphene bubbles have been observed in experiments, which can be used to determine the mechanical and adhesive properties of graphene. A nonlinear plate theory is adapted to describe the deformation of a graphene monolayer subject to lateral loads, where the bending moduli of monolayer graphene are independent of the in-plane Young's modulus and Poisson's ratio. A numerical method is developed to solve the nonlinear equations for circular graphene bubbles, and the results are compared to approximate solutions by analytical methods. Molecular dynamics simulations of nanoscale graphene bubbles are performed, and it is found that the continuum plate theory is suitable only within the limit of linear elasticity. Moreover, the effect of van der Waals interactions between graphene and its underlying substrate is analyzed, including large-scale interaction for nanoscale graphene bubbles subject to relatively low pressures.

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Figures

Grahic Jump Location
Fig. 1

Molecular dynamics simulation of a graphene bubble (gas molecules are green, fixed carbon atoms are cyan, and mobile carbon atoms are orange). The bubble radius is 10 nm, Ng = 225,000, and T = 300 K; the pressure is calculated to be 307.4 MPa. The inset shows the deflection profile of graphene along one diameter.

Grahic Jump Location
Fig. 2

(a) Calculated pressure in the MD simulation of a graphene bubble (a = 10 nm and T = 300 K); the dashed line is the pressure estimated by the ideal gas law. (b) Center deflection of the graphene bubble; the dashed line is the deflection calculated from the nonlinear plate theory using p = 307.4 MPa.

Grahic Jump Location
Fig. 3

Normalized deflection profiles of a graphene bubble (a = 10 nm) subject to increasing pressure, comparing the numerical results to the analytical solutions in Eqs. (3.2) and (3.4), from the linear plate solution and the approximate membrane analysis, respectively

Grahic Jump Location
Fig. 4

(a) Normalized center deflection versus pressure for graphene bubbles; (b) normalized pressure as a function of the center deflection. The numerical results are plotted as symbols, and the analytical solutions as lines. The solid line is the fitting by Eq. (6.1) with A = 3.09 and B = 5.47.

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Fig. 5

Strain distributions in graphene bubbles subject to increasing pressure (a) a = 10 nm and (b) a = 1000 nm

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Fig. 6

(a) Center strain as a function of the normalized pressure; (b) center strain versus h/a

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Fig. 7

Comparison of the deflection profiles for a graphene bubble (a = 10 nm). MD results in symbols and the numerical results from the nonlinear plate theory in solid lines.

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Fig. 8

Pressure versus center deflection from MD simulations of a graphene bubble (a = 10 nm), in comparison with the numerical solutions based on the nonlinear plate theory

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Fig. 9

(a) Effect of the vdW interaction on the deflection profile of a graphene bubble (a = 10 nm); (b) distributions of the vdW force intensity

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Fig. 10

Effect of the vdW interaction on center deflection of a graphene bubble (a = 10 nm)

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