Title:Stress focusing in a stamped circular sheet

Abstract:

A crumpled ball of paper is a mess of sharp creases and points where energy and stress are concentrated. On the other hand, a pristine sheet can be rolled into a tube – a smooth deformation that harbors no lasting damage. Recent work has established empirical criteria for when a confined sheet will form sharp crumples or smooth wrinkles, but those results do not address cases where the boundary of the film is tension-free. Here we present experiments where a thin polyester film is compressed in the thin gap between a concave and convex glass lens. We observe a transition between smooth wrinkles and sharp crumples at a threshold gap that depends on the sheet’s thickness and the substrate curvature. A previous version of this experiment reported a preliminary empirical scaling law for this transition; here we have reduced mechanical compliance in our setup to obtain tighter bounds on the scaling relation. Our measurements provide a foothold for a theory of stress focusing in geometrically-confined solids, which could aid the design of wearable sensors and inflatable structures.