Wrinkling, crumpling, folding, and all that: Pattern formation on thin sheets
Benny Davidovitch, UMass, Amherst

The complex morphologies of thin sheets consist of wrinkles, crumples, folds, creases, and blisters. These descriptive words may sound lucid – but do they carry any quantitatively distinguishable content? Following the classical approach of pattern formation theory, we seek to impart a universal meaning to these modes of deformation as distinct types of symmetry‐breaking instabilities of a flat, featureless sheet. This idea motivates us to consider the general problem of an axisymmetric stretching of a sheet. A familiar realization of this problem is the “map maker’s conflict”: projecting a flat sheet onto a foundation of spherical shape. Another representative realization is the Lame’ set‐up: exerting a radial tension gradient on a sheet, which may be free‐standing or resting on a solid or liquid foundation. Capillary forces provide a natural tool to study these and other realizations of the axisymmetric stretching problem. Furthermore, the singular behavior of sheets as their thickness becomes exceedingly small appears to generate a new playground for unexplored capillary effects. In this talk I will describe some key experiments in which capillary forces are used to probe the basic instabilities of stressed sheets, and some lessons drawn from our observations. I will introduce a set of morphologically‐relevant parameters that underlie the development of complex patterns in these experiments, and will show how wrinkling, crumpling, and possibly other deformation types can be understood as primary and secondary instabilities in a universal phase space spanned by those parameters.