Original Article
  • Coupled Wrinkling and Bending in Strain-Mismatched Tri-Layer Structures

  • Hyunsu Kwak*# , Junsik Kim*# , Anna Lee*†

  • * Department of Mechanical Engineering, POSTECH

  • This article is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

References
  • 1. Jia, Z., Peng, C., Lou, J., and Li, T., “A map of competing buckling-driven failure modes of substrate-supported thin brittle films,” Thin Solid Films, Vol. 520, No. 21, 2012, pp. 6576-6580.
  •  
  • 2. Zhao, Z., Fu, H., Tang, R., Zhang, B., Chen, Y., and Jiang, J., “Failure mechanisms in flexible electronics,” International Journal of Smart and Nano Materials, Vol. 14, No. 4, 2023, pp. 510-565.
  •  
  • 3. Yang, S., Khare, K., and Lin, P.C., “Harnessing surface wrinkle patterns in soft matter,” Advanced Functional Materials, Vol. 20, No. 16, 2010, pp. 2550-2564.
  •  
  • 4. Liu, N., Lu, Y. Li, Z., Zhao, H., Yu, Q., Huang, Y., Yang, J., and Huang, L., “Smart wrinkled interfaces: patterning, morphing, and coding of polymer surfaces by dynamic anisotropic wrinkling,” Langmuir, Vol. 40, No. 36, 2024, pp. 18837-18856.
  •  
  • 5. Lee, J., Park, H., Kim, S., Liu, C., Li, Z., and Sim, K., “Irreproducible SEBS wrinkling based on spin evaporation enabling identifiable artificial finger pad electronics,” Nature Communications, Vol. 16, No. 1, 2025, 2225.
  •  
  • 6. Cai, Y.W., Zhang, X.N., Wang, G.G., Li, G.Z., Zhao, D.Q., Sun, N., Li, F., Zhang, H.Y., Han, J.C., and Yang, Y., “A flexible ultra-sensitive triboelectric tactile sensor of wrinkled PDMS/MXene composite films for E-skin,” Nano Energy, Vol. 81, 2021, 105663.
  •  
  • 7. Wu, K., Sun, Y., Yuan, H., Zhang, J., Liu, G., and Sun, J., “Harnessing dynamic wrinkling surfaces for smart displays,” Nano Letters, Vol. 20, No. 6, 2020, pp. 4129-4135.
  •  
  • 8. Choi, S., Jo, W., Jeon, Y., Kwon, S., Kwon, J.H., Son, Y.H., Kim, J., Park, J.H., Kim, H., Lee, H.S., Nam, M., Jeong, E.G., Shin, J.B., Kim, T.S., and Choi, K.C., “Multi-directionally wrinkle-able textile OLEDs for clothing-type displays,” npj Flexible Electronics, Vol. 4, No. 1, 2020, 33.
  •  
  • 9. Noh, Y., Lee, G., Lee, H., and Lee, D., “Printable stretchable serpentine electrodes incorporating support patterns for stretchable elecronics,” ACS Applied Materials & Interfaces, Vol. 17, No. 45, 2025, pp. 62733-62742.
  •  
  • 10. Kim, J., Choi, H.W., Kim, B., Kim, E., and Kim, J., “Flexible electrode on e-textile based on screen-printed silver ink carbon nanotube,” The International Journal of Advanced Manufacturing Technology, Vol. 134, No. 1, 2024, pp. 127-137.
  •  
  • 11. Qian, J., Chen, Q., Hong, M., Xie, W., Jing, S., Bao, Y., Chen, G., Pang, Z., Hu, L., and Li, T., “Toward stretchable batteries: 3D-printed deformable electrodes and separator enabled by nanocellulose,” Materials Today, Vol. 54, 2022, pp. 18-26.
  •  
  • 12. Budday, S., Andres, S., Walter, B., Steinmann., P., and Kuhl, E., “Wrinkling instabilities in soft bilayered systems,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 375, No. 2093, 2017, 20160163.
  •  
  • 13. Auguste, A., Jin, L., Suo, Z., and Hayward, R.C., “The role of substrate pre-stretch in post-wrinkling bifurcations,” Soft Matter, Vol. 10, No. 34, 2014, pp. 6520-6529.
  •  
  • 14. Jiao, R., Wang, R., Wang, Y., Cheung, Y.K., Chen, X., Wang, X., Deng, Y., and Yu, H., “Vertical serpentine interconnect-enabled stretchable and curved electronics,” Microsystems & Nanoengineering, Vol. 9, 2023, 149.
  •  
  • 15. Xu, S., Zhang, Y., Cho, J., Lee, J., Huang, X., Jia, L., Fan, J.A., Su, Y., Su, J., Zhang, H., Cheng, H., Lu, B., Yu, C., Chuang, C., Kim, T., Song, T., Shigeta, K., Kang, S., Dagdeviren, C., Petrov, I., Braun, P.V., Huang, Y., Paik, U., and Rogers, J.A., “Stretchable batteries with self-similar serpentine interconnects and integrated wireless recharging systems,” Nature Communications, Vol. 4, 2013, 1543.
  •  
  • 16. Kim, D. H., Lu, N., Ghaffari, R., Kim, Y.S., Lee, S.P., Xu, L., Wu, J., Kim, R.H., Song, J., Liu, Z., Viventi, J., Graff, B., Elolampi, B., Mansour, M., Slepian, M.J., Hwang, S., Moss, J.D., Won, S.M., Huang, Y., Litt, B., and Rogers, J.A., “Materials for multifunctional balloon catheters with capabilities in cardiac electrophysiological mapping and ablation therapy,” Nature Materials, Vol. 10, 2011, pp. 316-323.
  •  
  • 17. Huang, Y., Su, Y.W., and Jiang, S., “Neutral layer design for flexible electronics,” Flexible Electronics: Theory and Method of Structural Design, Singapore: Springer Nature Singapore, 2023, pp. 321-349.
  •  
  • 18. Wu, M., Jian, M., Zhang, J., and Yang, L., “Optimizing bendability of flexible electronic devices using a neutral layer strategy,” Moore and More, Vol. 2, 2025, 2.
  •  
  • 19. Huang, Z.Y., Hong, W., and Suo, Z., “Nonlinear analyses of wrinkles in a film bonded to a compliant substrate,” Journal of the Mechanics and Physics of Solids, Vol. 53, No. 9, 2005, pp. 2101–2118.
  •  
  • 20. Cao, Y., and Hutchinson, J.W., “Wrinkling phenomena in neo-Hookean film/substrate bilayers,” Journal of Applied Mechanics, Vol. 79, 2012, 031019.
  •  
  • 21. Jiang, H., Khang, D.Y., Song, J., Sun, Y., Huang, Y., and Rogers, J.A., “Finite deformation mechanics in buckled thin films on compliant supports,” Proceedings of the National Academy of Sciences, Vol. 104, No. 40, 2007, pp. 15607–15612.
  •  
  • 22. Song, J., Jiang, H., Liu, Z.J., Khang, D.Y., Huang, Y., Rogers, J.A., and Koh, C., “Buckling of a stiff thin film on a compliant substrate in large deformation,” International Journal of Solids and Structures, Vol. 45, No. 10, 2008, pp. 3107–3121.
  •  
  • 23. Li, K., Cheng, X., Zhu, F., Li, L., Xie, Z., Luan, H., and Zhang, Y., “A generic soft encapsulation strategy for stretchable electronics,” Advanced Functional Materials, Vol. 29, No. 8, 2019, 1806630.
  •  
  • 24. Xu, R., Lee, J.W., Pan, T., Ma, S., Wang, J., Han, J.H., and Huang, Y., “Designing thin, ultrastretchable electronics with stacked circuits and elastomeric encapsulation materials,” Advanced Functional Materials, Vol. 27, No. 4, 2017, 1604545.
  •  
  • 25. Cheng, H., Zhang, Y., Hwang, K.C., Rogers, J.A., and Huang, Y., “Buckling of a stiff thin film on a pre-strained bi-layer substrate,” International Journal of Solids and Structures, Vol. 51, No. 18, 2014, pp. 3113–3118.
  •  
  • 26. Jiang, H., Sun, Y., Rogers, J.A., and Huang, Y., “Post-buckling analysis for the precisely controlled buckling of thin film encapsulated by elastomeric substrates,” International Journal of Solids and Structures, Vol. 45, No. 7–8, 2008, pp. 2014–2023.
  •  
  • 27. Kwak, H., Lee, J., Kim, J., Jo, H., Ki, K., and Lee, A., “Wrinkling of Thin Films in Pre-stretched Soft Substrate Trilayers,” International Journal of Mechanical Sciences, 2026, 111213.
  •  
  • 28. Yuan, X., Zhao, P., and Wang, Y., “Buckling of a Stiff Thin Film Embedded Between Two Compliant Substrates,” International Journal of Applied Mechanics, Vol. 15, No. 3, 2023, 2350027.
  •  
  • 29. Yuan, X., Zhao, P., Fan, Q., Wang, Y., and Li, X., “Theoretical and numerical analysis on buckling instability in a thin film sandwiched between two finite-thickness substrates under in-plane compression,” International Journal of Solids and Structures, Vol. 304, 2024, 113037.
  •  
  • 30. Zhou, Y., Xu, Y., Gong, H., and Wang, C., “Prediction and Regulation of Delamination at Flexible Film/Finite-Thickness-Substrate Structure Interfaces,” Acta Mechanica Solida Sinica, Vol. 37, No. 2, 2024, pp. 238–251.
  •  
  • 31. Ma, Y., Xue, Y., Jang, K.I., Feng, X., Rogers, J.A., and Huang, Y., “Wrinkling of a stiff thin film bonded to a pre-strained, compliant substrate with finite thickness,” Proceedings of the Royal Society A, Vol. 472, No. 2192, 2016.
  •  
  • 32. Lin, J., Guo, Q., Dou, S., Hua, N., Zheng, C., Pan, Y., and Chen, W., “Bistable structures with controllable wrinkled surface,” Extreme Mechanics Letters, Vol. 36, 2020, 100653.
  •  
  • 33. Timoshenko, S.P., and Gere, J.M., Theory of elastic stability. McGraw–Hill, New York, 1961.
  •  
  • 34. Yang, J.W., and Nie, G.H., “Analysis of sinusoidal interfacial wrinkling of an anisotropic film sandwiched between two compliant layers,” Journal of Applied Mechanics, Vol. 81, No. 9, 2014, 091013.
  •  

This Article

Correspondence to

  • Anna Lee

  • * Department of Mechanical Engineering, POSTECH

  • E-mail: annalee@postech.ac.kr