Abstract
A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if , the disc can fold into one of a discrete infinite number of states if . We construct these states in the regime where bending dominates and determine their energies and how stress is distributed in them. For each state a critical value of is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.
- Received 7 July 2008
DOI:https://doi.org/10.1103/PhysRevLett.101.156104
©2008 American Physical Society