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Finite Deformation Mechanics in Buckled Thin Films on Compliant Supports

Hanqing Jiang's picture

Nonlinear buckling of thin,
high modulus plates on compl
supports represents a classical problem in mechanics. In a recent article published in PNAS, coauthored by Hanqing Jiang, Dahl-Young Khang, Jizhou Song, Yugang Sun, Yonggang Huang and John A. Rogers, a finite deforamtion analysis was presented to accurately re-examine the stiff thin film/compliant substrate system (  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) (PDMS) 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.  We extended the previous small deformation analysis (e.g.,
Huang, Z. Y., Hong, W.,
& Suo, Z. (2005) J. Mech. Phys.
53, 2101-2118;
Chen, X. & Hutchinson, J. W. (2004) J. Appl. Mech.-Trans. ASME
71, 597-603), to finite deformation and considered both geometrical and materials
nonlinearities.  This finite deformation analysis 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. 


Recently we studied the effect of bonded strip width on buckling wavelength and got a semi-analytical solution for this problem. For narrow strips the wavelength and critical strain are function of strip width. However in most cases you won’t see difference, since this effect becomes noticeable when width is smaller than buckling wavelength. In your experiments the ribbons are almost narrow enough to see the difference. Have you tried to test ribbons of different width (more narrow than you show in paper)?

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