Postbuckling analysis and its application to stretchable electronics

Yewang Su, Jian Wu, Zhichao Fan, Keh Chih Hwang*, Jizhou Song, Yonggang Huang, John A. Rogers

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

108 Scopus citations


A versatile strategy for fabricating stretchable electronics involves controlled buckling of bridge structures in circuits that are configured into open, mesh layouts (i.e. islands connected by bridges) and bonded to elastomeric substrates. Quantitative analytical mechanics treatments of the responses of these bridges can be challenging, due to the range and diversity of possible motions. Koiter (1945) pointed out that the postbuckling analysis needs to account for all terms up to the 4th power of displacements in the potential energy. Existing postbuckling analyses, however, are accurate only to the 2nd power of displacements in the potential energy since they assume a linear displacementcurvature relation. Here, a systematic method is established for accurate postbuckling analysis of beams. This framework enables straightforward study of the complex buckling modes under arbitrary loading, such as lateral buckling of the island-bridge, mesh structure subject to shear (or twist) or diagonal stretching observed in experiments. Simple, analytical expressions are obtained for the critical load at the onset of buckling, and for the maximum bending, torsion (shear) and principal strains in the structure during postbuckling.

Original languageEnglish (US)
Pages (from-to)487-508
Number of pages22
JournalJournal of the Mechanics and Physics of Solids
Issue number3
StatePublished - Mar 2012


  • Diagonal stretching
  • Higher-order terms in curvature
  • Lateral buckling
  • Postbuckling
  • Stretchable electronics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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