Post-wrinkling behaviors of a bilayer on a soft substrate

Youlong CHEN, Xiangbiao LIAO*, Wei ZHAO, Pengfei YANG, Hang XIAO, Yilun LIU*, Xi CHEN

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

8 Citations (Scopus)


The instability behavior of a compressive bilayer on a soft substrate is of significance for epidermal electronics adhered to human skin. Conventionally, two different wrinkling modes dependent of the modulus of intermediate layer were proposed to evolve from flat feature. Here, we uncover a new periodic pattern of secondary wrinkling feature with further compression in the case of a moderate-modulus intermediate layer. FEM simulation results illustrate a linear relationship between this wavelength of secondary wrinkling and the modulus of intermediate layer. An analytical model based on Timoshenko beam theory is utilized to predict the wavelength and critical strain of this secondary wrinkling, which agrees well with that in FEM simulations. Further, a phase diagram of instability feature in the system of bilayer/soft substrate is proposed. The secondary wrinkling feature with such large wavelength has broad applications in tunable surface morphologies for smart glasses, color controlling and manipulation of water droplets. © 2021 Elsevier Ltd
Original languageEnglish
Pages (from-to)74-79
Number of pages6
JournalInternational Journal of Solids and Structures
Early online date8 Jan 2021
Publication statusPublished - Apr 2021
Externally publishedYes

Bibliographical note

The authors acknowledge the support of the National Natural Science Foundation of China (11572238). The work of X.L. and X.C. was supported by the Yonghong Zhang Family Center for Advanced Materials for Energy and Environment. X.L. acknowledges support from the China Scholarship Council (CSC) graduate scholarship.


  • Bilayer
  • Buckling mode
  • Phase diagram
  • Post-wrinkling
  • Soft substrate


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