Finite deformation mechanics in buckled thin films on compliant supports

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 104; no. 40; pp. 15607 - 15612
• Main Authors: Jiang, Hanqing, Khang, Dahl-Young, Song, Jizhou, Sun, Yugang, Huang, Yonggang, Rogers, John A
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 02-10-2007; National Acad Sciences
• Subjects: Accordions; Amplitude; Binding Sites; Buckling; Deformation; Dimethylpolysiloxanes - chemistry; Elasticity; Engineering - methods; Fracture mechanics; Material films; Materials science; Mechanical engineering; Microscopy, Atomic Force; Microscopy, Electron, Scanning; Models, Molecular; Models, Theoretical; Physical Sciences; Polycrystals; Silicones - chemistry; Stress, Mechanical; Studies; Thin films; Wavelengths
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0702927104

We present detailed experimental and theoretical studies of the mechanics of thin buckled films on compliant substrates. In particular, accurate measurements of the wavelengths and amplitudes in structures that consist of thin, single-crystal ribbons of silicon covalently bonded to elastomeric substrates of poly(dimethylsiloxane) reveal responses that include wavelengths that change in an approximately linear fashion with strain in the substrate, for all values of strain above the critical strain for buckling. Theoretical reexamination of this system yields analytical models that can explain these and other experimental observations at a quantitative level. We show that the resulting mechanics has many features in common with that of a simple accordion bellows. These results have relevance to the many emerging applications of controlled buckling structures in stretchable electronics, microelectromechanical systems, thin-film metrology, optical devices, and others.