Abstract :

Thin sheets assume a rich diversity of shapes in the natural world, ranging from folds on the earth's crust, to the wavy shapes of leaves and flowers, down to more microscopic biomembranes and synthetic thin films. The patterns often include smooth architectural motifs such as wrinkles, as well as focused localized objects such as folds and ridges. I will describe the emergence of complex shapes from featureless initial conditions in a series of experiments on ultra-thin polystyrene sheets floating on a fluid interface. A correct understanding of patterns in very thin sheets requires an approach entirely different from traditional theories of buckling. Our works provides a new definition of "very thin" in terms of a dimensionless group called the bendability. Many technological and natural instances of wrinkles fall within this regime of high bendability.