Technical Briefs

A Simply Analytic Study of Buckled Thin Films on Compliant Substrates

[+] Author and Article Information
Huanyu Cheng

Departments of Mechanical Engineering and
Civil and Environmental Engineering,
Center for Engineering and Health, and
Skin Disease Research Center,
Northwestern University,
Evanston, IL 60208

Jizhou Song

Department of Mechanical and Aerospace Engineering,
University of Miami,
Coral Gables, FL 33146
e-mail: jsong8@miami.edu

1Corresponding author.

Manuscript received August 19, 2013; final manuscript received August 21, 2013; accepted manuscript posted August 28, 2013; published online October 29, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(2), 024501 (Oct 29, 2013) (3 pages) Paper No: JAM-13-1349; doi: 10.1115/1.4025306 History: Received August 19, 2013; Revised August 21, 2013; Accepted August 28, 2013

Buckling of stiff thin films on compliant substrates enables many new applications, such as stretchable electronics. Song et al. [2008, “Buckling of a Stiff Thin Film on a Compliant Substrate in Large Deformation,” Int. J. Solids Struct., 45(10), pp. 3107–3121] developed a finite deformation theory to explain the buckled amplitude and wavelength very well. This theory not only accounts for finite geometry change, but also the finite strain and a nonlinear constitutive model for the substrate. To provide a better physical insight, this paper investigates those three effects, and shows that finite geometry change dominates in the finite deformation theory and the simplified analysis leads to results that agree well with experiments and the finite element method.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Bowden, N., Brittain, S., Evans, A. G., Hutchinson, J. W., and Whitesides, G. M., 1998, “Spontaneous Formation of Ordered Structures in Thin Films of Metals Supported on an Elastomeric Polymer,” Nature, 393(6681), pp. 146–149. [CrossRef]
Wang, Y., Feng, X., Lu, B., and Wang, G., 2013, “Surface Effects on the Mechanical Behavior of Buckled Thin Film,” ASME J. Appl. Mech., 80(2), p. 021002. [CrossRef]
Chen, C., Tao, W., Su, Y., Wu, J., and Song, J., 2013, “Lateral Buckling of Interconnects in a Noncoplanar Mesh Design for Stretchable Electronics,” ASME J. Appl. Mech., 80(4), p. 041031. [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(7205), pp. 748–753. [CrossRef] [PubMed]
Kim, R. H., Bae, M. H., Kim, D. G., Cheng, H., Kim, B. H., Kim, D. H., Li, M., Wu, J., Du, F., Kim, H. S., Kim, S., Estrada, D., Hong, S. W., Huang, Y., Pop, E., and Rogers, J., 2011, “Stretchable, Transparent Graphene Interconnects for Arrays of Microscale Inorganic Light Emitting Diodes on Rubber Substrates,” Nano Lett., 11(9), pp. 3881–3886. [CrossRef] [PubMed]
Kim, D.-H., Lu, N., Ma, R., Kim, Y.-S., Kim, R.-H., Wang, S., Wu, J., Won, S. M., Tao, H., Islam, A., Yu, K. J., Kim, T.-I., Chowdhury, R., Ying, M., Xu, L., Li, M., Chung, H.-J., Keum, H., Mccormick, M., Liu, P., Zhang, Y.-W., Omenetto, F. G.Huang, Y.Coleman, T., and Rogers, J. A., 2011, “Epidermal Electronics,” Science, 333(6044), pp. 838–843. [CrossRef] [PubMed]
Song, J., Jiang, H., Liu, Z. J., Khang, D. Y., Huang, Y., Rogers, J. A., Lu, C., and Koh, C. G., 2008, “Buckling of a Stiff Thin Film on a Compliant Substrate in Large Deformation,” Int. J. Solids Struct., 45(10), pp. 3107–3121. [CrossRef]
Jiang, H. Q., Khang, D. Y., Song, J. Z., Sun, Y. G., Huang, Y. G., and Rogers, J. A., 2007, “Finite Deformation Mechanics in Buckled Thin Films on Compliant Supports,” Proc. Natl. Acad. Sci. USA, 104, pp. 15607–15612. [CrossRef]
Yang, S. Y., Carlson, A., Cheng, H., Yu, Q., Ahmed, N., Wu, J., Kim, S., Sitti, M., Ferreira, P. M., Huang, Y., and Rogers, J. A., 2012, “Elastomer Surfaces With Directionally Dependent Adhesion Strength and Their Use in Transfer Printing With Continuous Roll-to-Roll Applications,” Adv. Mater., 24, pp. 2117–2122. [CrossRef] [PubMed]
Kim, S., Carlson, A., Cheng, H., Lee, S., Park, J.-K., Huang, Y., and Rogers, J. A., 2012, “Enhanced Adhesion With Pedestal-Shaped Elastomeric Stamps for Transfer Printing,” Appl. Phys. Lett., 100(17), pp. 171909. [CrossRef]
Cheng, H., Wu, J., Yu, Q., Kim-Lee, H.-J., Carlson, A., Turner, K. T., Hwang, K.-C., Huang, Y., and Rogers, J. A., 2012, “An Analytical Model for Shear-Enhanced Adhesiveless Transfer Printing,” Mech. Res. Commun., 43, pp. 46–49. [CrossRef]
Huang, Z., Hong, W., and Suo, Z., 2005, “Nonlinear Analyses of Wrinkles in a Film Bonded to a Compliant Substrate,” J. Mech. Phys. Solids, 53(9), pp. 2101–2118. [CrossRef]
Jiang, H. Q., Sun, Y. G., Rogers, J. A., and Huang, Y. G., 2008, “Post-Buckling Analysis for the Precisely Controlled Buckling of Thin Film Encapsulated by Elastomeric Substrates,” Int. J. Solids Struct., 45(7–8), pp. 2014–2023. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic illustration of the process for fabricating buckled thin films on compliant substrates with (a)-(b) prestrain strategy and (c) postbuckling upon applied strain

Grahic Jump Location
Fig. 2

Wavelength and amplitude as a function of prestrain

Grahic Jump Location
Fig. 3

Wavelength and amplitude as a function of applied strain with a prestrain of 16.2%




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