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Spontaneous wrinkling pattern of a constrained thin film membrane

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Abstract

The wrinkling morphology of an inhomogeneously constrained thin film membrane is explored using finite element simulations, where a small circular area in a thin sheet undergoes expansion, and buckles emerge due to differential in-plane deformation. The local wrinkling patterns are characterized by the normalized circular (inner) area size, the modulus mismatch between the inner and outer regions, and the normalized stress in the inner area. As the stress increases, the morphology transits from ripple-like to petal-like and finally to a branched pattern. Through parametric studies, the effect of the governing variables on the pattern evolution, wave number, and maximum deflection is discussed. The model is used to qualitatively explain the delamination/blister morphology observed in thin film/substrate systems. The study has the potential of inspiring new fabrication techniques based on mechanical self-assembly.

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References

  1. T.A. Witten, Rev. Mod. Phys. 79, 643 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. J. Huang, M. Juszkiewicz, W.H. de Jeu, E. Cerda, T. Emrick, N. Menon, T.P. Russell, Science 317, 650 (2007)

    Article  ADS  Google Scholar 

  3. L. Pocivavsek, R. Dellsy, A. Kern, S. Johnson, B. Lin, K.Y.C. Lee, E. Cerda, Science 320, 912 (2008)

    Article  ADS  Google Scholar 

  4. T. Tallinen, J.A. Astrom, J. Timonen, Nat. Mater. 8, 25 (2009)

    Article  ADS  Google Scholar 

  5. G.A. Vliegenthart, G. Gompper, Nat. Mater. 5, 216 (2006)

    Article  ADS  Google Scholar 

  6. M.K. Small, W.D. Nix, J. Mater. Res. 7, 1553 (1992)

    Article  ADS  Google Scholar 

  7. Y. Xiang, X. Chen, J.J. Vlassak, J. Mater. Res. 20, 2360 (2005)

    Article  ADS  Google Scholar 

  8. H. Lee, B. Jung, D. Kim, H. Park, Int. J. Precis. Eng. Manuf. 12, 865 (2011)

    Article  Google Scholar 

  9. E. Cerda, L. Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)

    Article  ADS  Google Scholar 

  10. E. Sharon, B. Roman, M. Marder, G. Shin, H.L. Swinney, Nature 419, 579 (2002)

    Article  ADS  Google Scholar 

  11. H. Liang, L. Mahadevan, Proc. Natl. Acad. Sci. USA 106, 22049 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. E. Sharon, B. Roman, H.L. Swinney, Phys. Rev. E 75, 046211 (2007)

    Article  ADS  Google Scholar 

  13. T. Mora, A. Boudaoud, Eur. Phys. J. E 20, 119 (2006)

    Article  Google Scholar 

  14. Z.S. Liu, W. Hong, Z.G. Suo, S. Swaddiwudhipong, Y.W. Zhang, Comput. Mater. Sci. 49, S60 (2010)

    Article  Google Scholar 

  15. Y. Klein, E. Efrati, E. Sharon, Science 315, 1116 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. E. Sharon, E. Efrati, Soft Mater. 6, 5693 (2010)

    Article  ADS  Google Scholar 

  17. S. Edmondson, K. Frieda, J.E. Comrie, P.R. Onck, W.T.S. Huck, Adv. Mater. 18, 724 (2006)

    Article  Google Scholar 

  18. J. Yin, Z. Cao, C. Li, I. Sheinman, X. Chen, Proc. Natl. Acad. Sci. 105, 19132 (2008)

    Article  ADS  Google Scholar 

  19. J. Yin, X. Chen, I. Sheinman, J. Mech. Phys. Solids 57, 1470 (2009)

    Article  ADS  MATH  Google Scholar 

  20. A.S. Argon, V. Gupta, H.S. Landis, J.A. Cornie, Mater. Sci. Eng. A 107, 41 (1989)

    Article  Google Scholar 

  21. K. Lee, S. Lee, D.-Y. Khang, T. Lee, Soft Mater. 6, 3249 (2010)

    Article  ADS  Google Scholar 

  22. X. Chen, J. Yin, Soft Mater. 6, 5667 (2010)

    Article  ADS  Google Scholar 

  23. H. Xiao, X. Chen, Soft Mater. 7, 10794 (2011)

    Article  ADS  Google Scholar 

  24. J. Yin, E. Bar-Kochba, X. Chen, Soft Mater. 5, 3469 (2009)

    Article  ADS  Google Scholar 

  25. J. Yin, X. Chen, J. Phys. D 43, 115402 (2010)

    Article  ADS  Google Scholar 

  26. J. Yin, X. Chen, J. Phys. D 44, 045401 (2011)

    Article  ADS  Google Scholar 

  27. J. Yin, X. Chen, Philos. Mag. Lett. 90, 423 (2010)

    Article  ADS  Google Scholar 

  28. J. Yin, G. Gerling, X. Chen, Acta Biomater. 6, 1487 (2010)

    Article  Google Scholar 

Download references

Acknowledgements

The work is supported by National Natural Science Foundation of China (11172231), Independent Innovation Fund of Shandong University (2011GN055), DARPA (W91CRB-11-C-0112), World Class University program through the National Research Foundation of Korea (R32-2008-000-20042-0), Changjiang Scholar Program from Ministry of Education of China, and National Science Foundation (CMMI-0643726). YY and BW are funded by the China Scholarship Council.

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Authors and Affiliations

  1. School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Yuan Yan & Tiejun Wang

  2. Department of Earth and Environmental Engineering, Columbia University, New York, NY, 10027, USA

    Binglei Wang, Jie Yin & Xi Chen

  3. Department of Engineering Mechanics, Shandong University, Jinan, Shandong, 250061, China

    Binglei Wang

  4. International Center for Applied Mechanics, SV Lab, Xi’an Jiaotong University, Xi’an, 710049, China

    Xi Chen

  5. Department of Civil & Environmental Engineering, Hanyang University, Seoul, 133-791, Korea

    Xi Chen

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  1. Yuan Yan
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  2. Binglei Wang
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  3. Jie Yin
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  4. Tiejun Wang
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  5. Xi Chen
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Correspondence to Xi Chen.

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Yan, Y., Wang, B., Yin, J. et al. Spontaneous wrinkling pattern of a constrained thin film membrane. Appl. Phys. A 107, 761–767 (2012). https://doi.org/10.1007/s00339-012-6921-7

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  • DOI: https://doi.org/10.1007/s00339-012-6921-7

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