Condensed Matter Physics Seminar: Imposing curved shapes on solid sheets: From instabilities to isometries

Abstract:

Imposing a curved shape on a solid sheet, generates in it elastic stress. This familiar motif is a consequence of Gauss’ theorema Egregium, which posits that there exists no isometric map between two surfaces of different Gaussian curvatures. This coupling between geometry (curvature) and mechanics (stress) underlies the morphological richness observed in solid sheets, and their nontrivial response to exerted forces.

In this talk I will attempt to provide a unifying framework for morphological transitions in elastic sheets, by demonstrating basic mechanisms through which a Gaussian curvature can (or cannot) be accommodated. I will present a few examples of elasto-capillary phenomena, and will discuss in depth a specific problem: the action of a point force (indentation) on a tensed sheet. 

Seminar Organizer: Prof. Shimshon Barad