Energy estimates for the von Kármán model of thin-film blistering

We consider the behavior of buckling driven thin-film blisterings using von Karman’s plate theory. Our focus is on the setting where the blistered region is the unit square with clamped boundary conditions at the vertical sides and periodic ones along the horizontal sides. In this setting, we prove rigorous upper and lower bounds for the elastic energy which are of the same order as the film thickness. We also present a convincing argument for the necessity of branching of folds near the boundary as has been observed in experiments.

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