Geometrically-frustrated wrinkle patterns 1: Defects and mesoscale structure*

Thin films readily buckle to relax compression, creating wrinkle patterns that can have considerable morphological complexity. Some of this complexity stems from a basic geometric conflict, arising when wrinkles that would otherwise prefer a fixed wavelength are formed in geometries where the lines of tension are splayed, for example when wrinkles emanate radially from a point. We study such frustrated states within an annular region of an elastic sheet subjected to unequal tensions at its inner and outer boundaries. Using experiments and simulations, we demonstrate two distinct solutions: (i) states with approximately constant wavelength, enabled by “defects” in the wrinkle pattern where new wrinkles begin, and (ii) “defect-free” states consisting of a fixed number of wrinkles of non-constant wavelength. We show how these two morphological types reflect distinct minima of a suitable coarse-grained elastic energy. We further predict a mesoscopic lengthscale for patches of nearly-parallel wrinkles separated by defect-rich regions, in agreement with our observations. This work unravels an organizing principle with analogs in liquid crystalline and superconducting states of matter. (This is part 1 in a 3-talk series).