Stress Focusing in Inflated Membranes: Threshold and Morphology*

Thin elastic films may undergo large-amplitude deformations even under small applied force, which makes their behaviors challenging to predict. A symmetry-breaking transition from smooth periodic wrinkles to sharp stress-focusing crumples was recently observed in experiments where an ultrathin polymer film was placed on a spherical water meniscus whose curvature was continuously increased [1]. However, a general set of conditions for crumple formation has remained elusive. We approach this problem on a different scale using ~10-cm-wide square membranes that we construct from polymer sheets, which we then inflate with air. As the internal pressure is gradually increased, sharp crumples form on the surface of sheet, which then transition to smooth wrinkles at higher pressure. Remarkably, all our data may be described by a single trend for the transition pressure, which depends linearly on the stretching modulus of the film and is inversely proportional to the size of the bag, where we have varied the sheet thickness, Young’s modulus, and bag size over a wide range. Finally, we use a 3D scanner to study the topography of the membrane as we go through the crumpling transition.
[1] King et al. PNAS 109 (2012).