Multiscale folding patterns in thin elastic sheets

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The derivation and the study of reduced theories for the elastic properties of thin films is a traditional field of (heuristic) multiscale analysis, dating back to Euler. A rigorous derivation of such models from three-dimensional elasticity theory is instead a recent development. The focus is on the case of compressive boundary conditions, which arise e.g. after deposition at high temperature on a substrate with a larger thermal expansion coefficient, cooling to room temperature and subsequent debonding. ... The work on energy scaling suggests but does not imply that asymptotically self-similar refinement of folds occurs near the boundaries of the debonded region without specifying the exponent; and that energy concentrates along the boundary and on a one-dimensional set in the interior part of the domain without specifying where. Both issues will be explored and the analysis will be extended to the case of anisotropic compression. ...