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Research Papers

Buckling of Multilayer Graphene Sheets Subjected to Axial Compression Based on a Continuum Mechanics Model

[+] Author and Article Information
Moonhong Kim

Department of Mechanical Engineering,
Korea Advanced Institute of Science
and Technology (KAIST),
291 Daehak-ro, Yuseong-gu,
Daejeon 34141, South Korea

Seyoung Im

Department of Mechanical Engineering,
Korea Advanced Institute of Science
and Technology (KAIST),
291 Daehak-ro, Yuseong-gu,
Daejeon 34141, South Korea
e-mail: sim@kaist.ac.kr

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 4, 2018; final manuscript received February 26, 2018; published online March 20, 2018. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 85(6), 061002 (Mar 20, 2018) (10 pages) Paper No: JAM-18-1008; doi: 10.1115/1.4039457 History: Received January 04, 2018; Revised February 26, 2018

Buckling of multilayer graphene sheets (MLGSs) subjected to an axial compressive load in plane-strain condition is studied. Closed-form solutions for buckling load of MLGSs are obtained based on a continuum model for MLGSs. Two different kinematic assumptions, which lead to MLGS beam, which was recently proposed by the authors, and the Euler beam, are used to obtain the buckling loads. The obtained solutions yield significantly different buckling loads when the axial length is small. To validate obtained results, molecular dynamics (MD) simulations are conducted, and they show that the MLGS beam model well captures the buckling load of MLGSs. The buckling solution of MLGS beam model provides two interesting facts. First, the buckling load of MLGSs coincides with the Euler buckling load when the length is large. Second, when the number of layers is large, the buckling strain converges to a finite value, and could be expressed as a linear combination of the buckling strain of single-layer graphene and the ratio between the shear rigidity of interlayer and the tensile rigidity of graphene layer. We validate the asymptotic behavior of buckling strain through MD simulations and show that buckling occurs even when the overall thickness is larger than the axial length. Finally, we present a diagram that contains buckling strain of MLGSs according to the boundary conditions, the number of layers, and the axial length.

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References

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Figures

Grahic Jump Location
Fig. 1

(a) The atomistic model of MLGSs at the undeformed configuration and (b) a continuum model for MLGSs in plane-strain at the undeformed configuration

Grahic Jump Location
Fig. 2

Kinematics of proposed MLGS beam model in plane-strain: (a) at the undeformed configuration and (b) at a deformed configuration

Grahic Jump Location
Fig. 5

Specimens for MD simulation of buckling of MLGSs: (a) at the undeformed configuration and (b) at a deformed configuration. The axial direction coincides with the armchair direction, N = 2, and L = 6.07 nm.

Grahic Jump Location
Fig. 4

Normalized buckling loads obtained from analytical solutions for two different kinematic models when both ends are clamped and N = 2

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Fig. 3

Free body diagram of buckled state of MLGSs

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Fig. 6

Normalized load versus normalized strain curve obtained by using MD when both ends are clamped and subjected to compression (N = 2 and L = 6.07 nm)

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Fig. 7

Normalized buckling loads of MLGSs obtained from the analytical solution and MD simulations according to the normalized length of beam and the number of layers

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Fig. 12

Kinematics of the Euler beam model for MLGSs in plane strain at a deformed configuration

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Fig. 8

Critical buckling strain according to the number of layers. The axial length is 3.98 nm, and both ends are subjected to the clamped condition.

Grahic Jump Location
Fig. 9

The buckled configuration of MLGSs having high thickness length ratio when ε=5εc, N = 15, L = 3.98 nm, and both ends are clamped

Grahic Jump Location
Fig. 10

Buckling mode shapes of MLGSs according to boundary conditions: (a) both ends pinned-end, (b) one end free and the other clamped, and (c) both clamped

Grahic Jump Location
Fig. 11

Critical buckling strains of MLGSs according to the boundary conditions, the number of layer, and the length

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