Self-similar structures near boundaries in strained systems.
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 sheet 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.
Audoly
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B
Laboratoire de modélisation en mécanique, UMR 7607 du CNRS, Université Pierre et Marie Curie, 4 place Jussieu, F-75252 Paris Cedex 05, France.
Boudaoud
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A