Multiscale folding patterns in thin elastic sheets

薄膜弹性特性的简化理论的推导和研究是启发式多尺度分析的一个传统领域，可以追溯到欧拉。从三维弹性理论中严格推导出这样的模型是最近的发展。重点是压缩边界条件的情况，例如在高温下沉积在具有较大热膨胀系数的基板上，冷却到室温并随后剥离. ...关于能量标度的研究表明，但并不意味着在不指定指数的情况下，在脱粘区域的边界附近会出现渐近自相似的褶皱细化；能量沿着边界集中在一维集合上集中在定义域的内部而不指定在哪里。这两个问题将进行探讨，并将分析扩展到各向异性压缩的情况. ...

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. ...