Research Papers

Mechanism of the Transition From In-Plane Buckling to Helical Buckling for a Stiff Nanowire on an Elastomeric Substrate

[+] Author and Article Information
Youlong Chen

International Center for Applied Mechanics,
SV Laboratory,
School of Aerospace,
Xi'an Jiaotong University,
No. 28, Xianning West Road,
Xi'an, Shaanxi 710049, China
e-mail: cyl.900125@stu.xjtu.edu.cn

Yong Zhu

Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Engineering Building 3,
Rm 3238 (Centennial Campus),
911 Oval Drive,
Raleigh, NC 27695
e-mail: yong_zhu@ncsu.edu

Xi Chen

Fellow ASME
Columbia Nanomechanics Research Center,
Department of Earth and
Environmental Engineering,
Columbia University,
500 West 120th Street,
New York, NY 10027
e-mail: xichen@columbia.edu

Yilun Liu

State Key Laboratory for Strength and
Vibration of Mechanical Structures,
School of Aerospace,
Xi'an Jiaotong University,
No. 28, Xianning West Road,
Xi'an, Shaanxi 710049, China
e-mail: yilunliu@mail.xjtu.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 2, 2015; final manuscript received January 22, 2016; published online February 10, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(4), 041011 (Feb 10, 2016) (6 pages) Paper No: JAM-15-1646; doi: 10.1115/1.4032573 History: Received December 02, 2015; Revised January 22, 2016

In this work, the compressive buckling of a nanowire partially bonded to an elastomeric substrate is studied via finite-element method (FEM) simulations and experiments. The buckling profile of the nanowire can be divided into three regimes, i.e., the in-plane buckling, the disordered buckling in the out-of-plane direction, and the helical buckling, depending on the constraint density between the nanowire and the substrate. The selection of the buckling mode depends on the ratio d/h, where d is the distance between adjacent constraint points and h is the helical buckling spacing of a perfectly bonded nanowire. For d/h > 0.5, buckling is in-plane with wavelength λ = 2d. For 0.27 < d/h < 0.5, buckling is disordered with irregular out-of-plane displacement. While, for d/h < 0.27, buckling is helical and the buckling spacing gradually approaches to the theoretical value of a perfectly bonded nanowire. Generally, the in-plane buckling induces smaller strain in the nanowire, but consumes the largest space. Whereas the helical mode induces moderate strain in the nanowire, but takes the smallest space. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and three-dimensional complex nanostructures.

Copyright © 2016 by ASME
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Fig. 1

Model of a SiNW partially bonded to the PDMS substrate. The dots represent the constraint between the SiNW and the PDMS substrate and the distance between the adjacent constraint points. A uniaxial compression is applied to the PDMS substrate in x direction.

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Fig. 2

The buckling modes of the SiNW partially bonded to a PDMS substrate. The dots represent the constraints (bonded sites) between the SiNW and the PDMS substrate. Color contour of the maximum principal strain in the buckled configuration is given.

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Fig. 3

The in-plane (uz) and out-of-plane (uy) displacements of SiNW corresponding to different modes in Fig. 2 (d = 1 μm, d = 0.5 μm, and d = 0.1 μm), respectively

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Fig. 4

The buckling wavelength of SiNW for different constraint densities. The horizontal dashed line indicates the theoretical buckling spacing h of the perfectly bonded SiNW and the oblique dashed line is 2d. Error bars are given for the out-of-plane disordered buckling mode.

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Fig. 5

The critical buckling strain of the partially bonded SiNW with different constraint densities. The smooth line (without squares) indicates the Euler beam buckling strain.

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Fig. 6

(a) The strain distributions along SiNW for the perfectly bonded SiNW and partially bonded SiNW (d = 2.5 μm, d = 0.5 μm) and (b) the maximum strain-maximum displacement relation for different constraint densities

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Fig. 7

The typical planar (a) and 3D (b) configuration of the SiNW for the helical buckling and (c) the in-plane buckling mode. The brightness represents the height of the substrate surface.

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Fig. 8

(a) The relations of the in-plane and out-of-plane displacement amplitudes to the effective compressive strain for the helical buckling obtained from FEM simulations. (b) The comparison of the in-plane and the out-of-plane displacement amplitudes between experiments (up various UVO treatment time) and FEM simulations. The shadow areas indicate the ranges obtained from FEM simulations.

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Fig. 9

The strain energy of three buckling modes for the constraint distance 2.5 μm, 0.5 μm and 0.1 μm, respectively. Forthe constraint distance 0.5 μm, the strain energy of the in-plane bucking mode is almost overwritten by the strain energy of the helical buckling mode with the constraint distance 0.1 μm.




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