c, thefilm buckles to relieve some of the strain; the membrane strain, mem, as evaluated at the plane that lies at the midpoint of thethickness of the film, remains and has a magnitude almost equal to  c. The peak strains  peak in the film are equal to the sum ofmembrane strain  mem and the strain induced by the buckledgeometry. In most cases of practical interest, the strain associatedwith the buckled geometry is much larger than  mem, thus this peakstrain can be written peak   2   pre c 1   1 3 1  pre. [5]The magnitude of  peak is typically much smaller than the overallstrain,  pre    mem, that the film accommodates by buckling. Forexample, in the case of  pre  28%,  peak is only 1.8%for the systemof Fig. 2. This mechanical advantage provides an effective level ofstretchability/compressibility in materials that are intrinsically brit-tle. As a result,  peak determines the point at which fracture occursin the film. For Si, the fracture strain is in the range of  fracture (foreither compression or tension). The maximum allowable prestrainis, therefore, approximately fracture24 c 1  4348 fracture24 c  ,which, for the system examined here, is  37% or almost 20 timeslarger than  fracture.Fig. 5A shows the  peak and  mem as a function of  pre. Themembrane strain is negligible compared with the peak strain.Likewise, the peak strain is much smaller than the prestrain, suchthat the system can accommodate large strains. The measuredcontour length of the buckled Si film on PDMS substrate, shown inFig. 5B, is approximately constant and is independent of theprestrain. This result is consistent with a negligibly small value for mem.Postbuckling Behavior. When the buckled system is subjected to anapplied strain  applied, the wavelength and amplitude become     0 1  applied 1  pre 1  applied  1/3,A   h   pre   applied / c   1 1  pre 1  applied  1/3,[6]where    5( pre    applied)(1    pre)/32. The amplitude A vanisheswhen the applied strain reaches the prestrain plus the critical strain c. In this situation, themembrane strain is equal to  c. Additionalapplied strain relaxes the membrane strain and then, ultimately,appears as tensile strain in the silicon up to the point of fracture.The peak strain in the film is peak   2    pre   applied c 1  applied  1/3 1  pre. [7]01230 10203040051015A λ Experiment Finite-Deform. Previous Model Accordion Model  e d u t i l p m A A (   µ ) m  h t g n e l e v a W λ (   µ ) mPrestrain εpre (%)Fig. 4. Wavelength and amplitude of buckled structures of Si (100 nmthickness) on PDMS as a function of the prestrain. The finite-deformationbuckling theory yieldswavelengths and amplitudes that both agreewellwithexperiments. Also shown are results from previous mechanics models (i.e.,small deformation limit) and the simple accordion model. Fig. 6 gives the experimentally measured and theoretically pre-dicted wavelength   and amplitude A versus applied strain  appliedfor a buckled Si thin-film/PDMS substrate formed with a prestrainof 16.2%, and other parameters the same as those of the examplesdescribed in the other sections. The constant wavelength and theamplitude predicted by the existingmechanicsmodels, given by Eq.2 with  pre replaced by  pre   applied, are also shown.