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Research Papers

Mechanics Interpretation on the Bending Stiffness and Wrinkled Pattern of Graphene

[+] Author and Article Information
Ran Xu

AML, CNMM
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Yu Wang

AML, CNMM
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
The key laboratory of Changcheng Institute of Metrology & Measurement (CIMM),
Beijing 100095, China

Bin Liu

AML, CNMM
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: liubin@tsinghua.edu.cn

Daining Fang

LTCS, College of Engineering,
Peking University,
Beijing 100871, China
e-mail: fangdn@pku.edu.cn

1Corresponding authors.

Manuscript received January 31, 2013; final manuscript received March 5, 2013; accepted manuscript posted April 10, 2013; published online May 31, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 040910 (May 31, 2013) (5 pages) Paper No: JAM-13-1053; doi: 10.1115/1.4024178 History: Received January 31, 2013; Revised March 05, 2013; Accepted April 10, 2013

In this paper we attempt to answer two questions on graphene from a mechanic's viewpoint: why does this one-atom-thick monolayer have finite bending stiffness to ensure its stability? and what is its wrinkle mechanism? As for the first question, it is found that the repulsive residual internal moment in the bond angle can lead to a nonzero bending stiffness, which makes the graphene flat. Together with long-range attraction among atoms, such as van der Waals forces, a graphene prefers to have a self-buckling wrinkled configuration with many waves.

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram of graphene with honeycomb lattice

Grahic Jump Location
Fig. 2

(a) A four-carbon-atom system of graphene, which can be treated as a structure with rods and spiral springs. (b) Possible new configuration of three atoms if one atom is removed, and the bond angle is not 120 deg or 2π/3 anymore.

Grahic Jump Location
Fig. 3

The central atom of the four-carbon-atom system is pulled out of the plane with the displacement v

Grahic Jump Location
Fig. 4

Schematic diagram of graphene under a slight pure bending

Grahic Jump Location
Fig. 5

The predicted bending stiffness of graphene monolayer as a function of the bending curvature

Grahic Jump Location
Fig. 6

The stable configurations of free standing graphene monolayer at 0 K with different residual internal moments: (a) M0=0, (b) M0=-kθπ/12, and (c) M0=-kθπ/6

Grahic Jump Location
Fig. 7

(a) The buckling configuration of a double layered plate with different thermal expansion; (b) the buckling pattern of expanding stiff thin film on soft substrate; (c) schematic diagram of the buckling configuration of a graphene; and (d) six possible local buckling patterns for small graphene patches

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