Elastic Building Blocks in a Wrinkle Cascade
Thursday, May 19, 2011 - 2:30pm - 3:00pm
Robert Schroll (University of Massachusetts)
Several features, such as d-cones, minimal ridges, developable patches, and collapsed compressive stress, occur regularly in the the configuration of elastic sheets. We dub such features building blocks. By understanding the shape of an elastic sheet as an amalgamation of these building blocks, we can understand its behavior without fully solving the governing equations. Here, we consider the building blocks that make up a wrinkle cascade. Such a cascade occurs when an elastic sheet is subject to confinement, so that it buckles at some optimal wavelength, but is required to have another wavelength at one end. The transition between imposed and optimal wavelength occurs in a cascade going through several intermediate wavelengths. We simulate a single generation of this cascade and demonstrate that it is composed of two different building blocks: a focused-stress feature reminiscent of a d-cone and a diffuse-stress feature. The former is characterized by a geometrical constraint (inextensibility), while the latter is governed by a mechanical constraint: the dominance of a single component of the stress tensor. We will discuss how boundary conditions affect which building blocks are chosen.