How to make a (designed) three-dimensional shape from a growing sheet
Wednesday, May 18, 2011 - 4:00pm - 4:30pm
Christian Santangelo (University of Massachusetts)
What three-dimensional shapes can be made with an elastic film of finite thickness upon which an isotropic, but inhomogeneous, pattern of growth has been prescribed? I will describe both theoretical progress in addressing this question, and an experimental realization in a swelling polymer film in which a metric is prescribed by modulating the local polymer cross-link density. By imposing a pattern of swelling dots, similar to half-toning in an inkjet printer, we can prescribe arbitrary swelling patterns. This system allows us to directly put mathematics to the experimental test. I will finally present a simple swelling geometry from which more complex shapes can be built, and rationalize some of the potentially counterintuitive behavior observed experimentally.