Self-similar folding patterns and energy scaling in compressed elastic sheets

摘要

Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debondedudfrom the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy withudrespect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached by self-similarudfolding patterns that refine towards the boundary, in agreement with experimental observations. We then extend theudanalysis to anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transitionudbetween a regime where the deformation is governed by global properties of the domain and another one where theuddirection of maximal compression dominates and the scale of the folds is mainly determined by the distance to theudboundary in the direction of the folds themselves.