A variational perspective on wrinkling patterns in thin elastic sheets

Wrinkling of thin elastic sheets can be viewed as a way how to avoid compressive stresses. While the question of where the wrinkles appear is well-understood, understanding properties of wrinkling is not trivial. Considering a variational viewpoint, the problem amounts to minimization of an elastic energy, which can be viewed as a non-convex membrane energy singularly perturbed by a higher-order bending term. To understand the global minimizer (ground state), the first step is to identify its energy, in particular its dependence on the small physical parameter (thickness). I will discuss several problems where the optimal energy scaling law was identified.