Biological & Soft Matter Seminar: Instabilities in thin elastic sheets

Abstarct:

The phenomenon of pattern formation in thin elastic sheets has been observed in a wide range of natural systems, such as the wrinkling of leaves, and the folding of biological membranes. At the same time, this process has important applications in technology, such as the design of microelectromechanical systems and the fabrication of stretchable electronics. Understanding the underlying mechanics of pattern formation in thin elastic sheets is therefore of great interest both from a fundamental scientific perspective and for practical engineering purposes. In this seminar, I will discuss two studies that investigate static and dynamic pattern formation in thin elastic sheets. In the first study, we explore the formation of a blister, which is a small, delaminated region, in a thin sheet that is adhered to a soft and adhesive substrate. We derive an approximate solution to this nonlinear problem and use our solution to investigate the flat-to-blister and the wrinkles-to-blister instabilities. In the second study, we investigate the snap-through instability of a thin sheet in a fluid medium. We explore how external pressure differences, material properties, and geometric factors influence the system's behavior. We discuss an unusual behavior of the system at the onset of the instability and show that it forms spikes of pressure-drop at the vicinity of the inverted configuration.