Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases.

Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in plant leaves and animal epithelia and perhaps even the formation of human fingerprints. We elucidate a primary source of this morphological complexity-an incompatibility between an elastically favored "microstructure" of uniformly spaced wrinkles and a "macrostructure" imparted through the wrinkle director and dictated by confinement forces. Our theory is borne out of experiments and simulations of floating sheets subjected to radial stretching. By analyzing patterns of grossly radial wrinkles we find two sharply distinct morphologies: defect-free patterns with a fixed number of wrinkles and nonuniform spacing and patterns of uniformly spaced wrinkles separated by defect-rich buffer zones. We show how these morphological types reflect distinct minima of a Ginzburg-Landau functional-a coarse-grained version of the elastic energy, which penalizes nonuniform wrinkle spacing and amplitude, as well as deviations of the actual director from the axis imposed by confinement. Our results extend the effective description of wrinkle patterns as liquid crystals [H. Aharoni et al, Nat. Commun. 8, 15809 (2017)], and we highlight a fascinating analogy between the geometry-energy interplay that underlies the proliferation of defects in the mechanical equilibrium of confined sheets and in thermodynamic phases of superconductors and chiral liquid crystals.

Geometry underlies the mechanical stiffening and softening of an indented floating film.

A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we study the indentation of a polymer film on a liquid bath. Our experiments and simulations support a recently-predicted stiffening response [D. Vella and B. Davidovitch, Phys. Rev. E, 2018, 98, 013003], and we show that the system softens at large slopes, in agreement with our theory that addresses small and large deflections. We show how stiffening and softening emanate from nontrivial yet generic features of the stress and displacement fields.