Research Papers

Lateral Buckling of Interconnects in a Noncoplanar Mesh Design for Stretchable Electronics

[+] Author and Article Information
Chi Chen

Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33146

Weiming Tao

Institute of Applied Mechanics,
Zhejiang University,
Hangzhou 310027, China

Yewang Su

Department of Mechanical Engineering and Department of Civil and Environmental Engineering,
Northwestern University,
Evanston, IL 60208;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Jian Wu

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China;
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Jizhou Song

Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33146
e-mail: j.song8@miami.edu

1Corresponding author.

Manuscript received October 26, 2012; final manuscript received November 19, 2012; accepted manuscript posted November 22, 2012; published online May 23, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 041031 (May 23, 2013) (6 pages) Paper No: JAM-12-1497; doi: 10.1115/1.4023036 History: Received October 26, 2012; Revised November 19, 2012; Accepted November 22, 2012

Analytical models have been established to study the lateral buckling of interconnects under shear in a noncoplanar mesh design for stretchable electronics. Analytical expressions are obtained for the critical load and buckling shape at the onset of buckling by solving the equilibrium equations. The postbuckling behavior is studied by energy minimization of the potential energy, including up to fourth power of the displacement. A simple expression of the amplitude characterizing the deformation after buckling is obtained. These results agree well with the finite element simulations without any parameter fitting. The models in this paper may provide a route to study complex buckling modes of interconnects, such as diagonal compression/stretching involving both compression and shear.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Crawford, G. P., 2005, Flexible Flat Panel Display Technology, Wiley, New York.
Jin, H. C., Abelson, J. R., Erhardt, M. K., and Nuzzo, R. G., 2004, “Soft Lithographic Fabrication of an Image Sensor Array on a Curved Substrate,” J. Vac. Sci. Technol. B, 22, pp. 2548–2551. [CrossRef]
Ko, H. C., Stoykovich, M. P., Song, J. Z., Malyarchuk, V., Choi, W. M., Yu, C. J., Geddes, J. B., Xiao, J. L., Wang, S. D., Huang, Y. G., and Rogers, J. A., 2008, “A Hemispherical Electronic Eye Camera Based on Compressible Silicon Optoelectronics,” Nature, 454, pp. 748–753. [CrossRef] [PubMed]
Jung, I., Xiao, J., Malyarchuk, V., Lub, C., Li, M., Liu, Z., Yoon, J., Huang, Y., and Rogers, J. A., 2011, “Dynamically Tunable Hemispherical Electronic Eye Camera System With Adjustable Zoom Capability,” Proc. Natl. Acad. Sci. U.S.A., 108, pp. 1788–1793. [CrossRef] [PubMed]
Viventi, J., Kim, D.-H., Moss, J. D., Kim, Y.-S., Blanco, J. A., Annetta, N., Hicks, A., Xiao, J., Huang, Y., Callans, D. J., Rogers, J. A., and Litt, B., 2010, “A Conformal, Bio-Interfaced Class of Silicon Electronics for Mapping Cardiac Electrophysiology,” Sci. Transl. Med., 2, p. 24ra22. [CrossRef] [PubMed]
Kim, D. H., Lu, N. S., Ghaffari, R., Kim, Y. S., Lee, S. P., Xu, L. Z., Wu, J. A., Kim, R. H., Song, J. Z., Liu, Z. J., Viventi, J., de Graff, B., Elolampi, B., Mansour, M., Slepian, M. J., Hwang, S., Moss, J. D., Won, S. M., Huang, Y. G., Litt, B., and Rogers, J. A., 2011, “Materials for Multifunctional Balloon Catheters With Capabilities in Cardiac Electrophysiological Mapping and Ablation Therapy,” Nature Mater., 10, pp. 316–323. [CrossRef]
Kim, D. H., Lu, N. S., Ma, R., Kim, Y. S., Kim, R. H., Wang, S. D., Wu, J., Won, S. M., Tao, H., Islam, A., Yu, K. J., Kim, T. I., Chowdhury, R., Ying, M., Xu, L. Z., Li, M., Chung, H. J., Keum, H., McCormick, M., Liu, P., Zhang, Y. W., Omenetto, F. G., Huang, Y. G., Coleman, T., and Rogers, J. A., 2011, “Epidermal Electronics,” Science, 333, pp. 838–843. [CrossRef] [PubMed]
Someya, T., Sekitani, T., Iba, S., Kato, Y., Kawaguchi, H., and Sakurai, T., 2004, “A Large-Area, Flexible Pressure Sensor Matrix With Organic Field-Effect Transistors for Artificial Skin Applications,” Proc. Natl. Acad. Sci. U.S.A., 101, pp. 9966–9970. [CrossRef] [PubMed]
Takei, K., Takahashi, T., Ho, J. C., Ko, H., Gillies, A. G., Leu, P. W., Fearing, R. S., and Javey, A., 2010, “Nanowire Active-Matrix Circuitry for Low-Voltage Macroscale Artificial Skin,” Nature Mater., 9, pp. 821–826. [CrossRef]
Nathan, A., Park, B., Sazonov, A., Tao, S., Chan, I., Servati, P., Karim, K., Charania, T., Striakhilev, D., Ma, Q., and Murthy, R. V. R., 2000, “Amorphous Silicon Detector and Thin Film Transistor Technology for Large-Area Imaging of X-Rays,” Microelectron. J., 31, pp. 883–891. [CrossRef]
Kim, D. H., Song, J., Choi, W. M., Kim, H. S., Kim, R. H., Liu, Z. J., Huang, Y., Hwang, K. C., Zhang, Y., and Rogers, J. A., 2008, “Materials and Noncoplanar Mesh Designs for Integrated Circuits With Linear Elastic Responses to Extreme Mechanical Deformations,” Proc. Natl. Acad. Sci. U.S.A., 105, pp. 18675–18680. [CrossRef] [PubMed]
Song, J., Huang, Y., Xiao, J., Wang, S., Hwang, K. C., Ko, H. C., Kim, D. H., Stoykovich, M. P., and Rogers, J. A., 2009, “Mechanics of Noncoplanar Mesh Design for Stretchable Electronic Circuits,” J. Appl. Phys., 105, p. 123516. [CrossRef]
Machado, S. P., and Cortínez, V. H., 2005, “Lateral Buckling of Thin-Walled Composite Bisymmetric Beams With Prebuckling and Shear Deformation,” Eng. Struct., 27, pp. 1185–1196. [CrossRef]
Sapountzakis, E. J., and Dourakopoulos, J. A., 2009, “Lateral Buckling Analysis of Beams of Arbitrary Cross Section by BEM,” Comput. Mech., 45, pp. 11–21. [CrossRef]
Su, Y., Wu, J., Fan, Z., Hwang, K. C., Song, J., Huang, Y., and Rogers, J. A., 2012, “Postbuckling Analysis and Its Applications to Stretchable Electronics,” J. Mech. Phys. Solids, 60, pp. 487–508. [CrossRef]
Timoshenko, S. P., and Gere, J. M., 1961, Theory of Elastic Stability, 2nd ed., McGraw-Hill, New York.
Pi, Y. L., and Trahair, N. S., 1992, “Energy Equation for Beam Lateral Buckling,” J. Struct. Eng., 18, p. 1462. [CrossRef]
Bazant, Z. P., and Cedolin, L., 2003, Stability of Structures, Dover, New York.
Dassault Systèmes, 2009, ABAQUS Analysis User's Manual V6.9, Dassault Systèmes, Pawtucket, RI.


Grahic Jump Location
Fig. 1

(a) A schematic diagram of noncoplanar mesh design with islands chemically bonded to the compliant substrate and the interconnects loosely bonded; (b) SEM image of noncoplanar mesh design under shear

Grahic Jump Location
Fig. 2

A schematic diagram of lateral buckling of a beam

Grahic Jump Location
Fig. 3

The buckling shape of rotation of the cross-section φ¯(s)

Grahic Jump Location
Fig. 4

The buckling shape of displacement of center in x direction u¯(s)

Grahic Jump Location
Fig. 5

The amplitude A versus the applied displacement v0 for the buckling mode 1 of a beam with L = 20, a = 1, b = 0.1, and ν = 0.3



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In