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From: Audoly, B., and Boudaoud, A., 2003, “Self-Similar Structures Near Boundaries in Strained Systems,” Phys. Rev. Lett., 91, p. 086105.
ABSTRACT: We study the buckling of thin elastic plates caused by residual strains concentrated near a free edge. This is a model for plant leaves and torn plastic sheets morphologies. We derive new governing equations explaining self-similar patterns reported earlier in experiments. We reveal the cascade mechanism, determine the bounds for its wavelengths and predict a similarity factor of 3 in agreement with experiments. This is confirmed by numerical solutions with up to five generations of wrinkles.
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