Localized patterns in crushed conical shells

¹ Paulson School of Engineering and Applied Sciences, Harvard University - Cambridge, MA 02138, USA
² Department of Computer Science, University of Texas at Austin - Austin, TX 78712, USA
³ Department of Physics, Harvard University - Cambridge, MA 02138, USA

^(a) shmuel@seas.harvard.edu
^(b) Lmahadev@g.harvard.edu

Received: 30 January 2018
Accepted: 19 September 2018

Abstract

We use experiments and numerical simulations to study the rapid buckling of thin-walled cones as they impact a solid surface at high velocities. The buildup of air pressure inside the cone localizes the deformations to the impacting interface with the solid surface, leading to the hierarchical formation of an ordered pattern of small rhomboidal cells. In contrast, when the inner air pressure is not allowed to develop, the ordered pattern is destabilized and the cone collapses in a highly disordered state on long length scales. Numerical simulations confirm that the transition between ordered and disordered crumpling is governed by the competition between the elastic deformation energy of the shells and the work required to pressurize the air. Our results show how dynamic stabilization via tensioning suppresses long wavelength subcritical instabilities in shells and leads to the localization and propagation of short wavelength patterns.