Conical defects in growing sheets

Mueller, Martin Michael; Amar, Martine Ben; Guven, Jemal

Conical defects in growing sheets

Authors

Mueller, Martin Michael

Amar, Martine Ben

Guven, Jemal

Description

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle $se$ at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if $se <= 0$, the disc can fold into one of a discrete infinite number of states if $se$ is positive. We construct these states in the regime where bending dominates, determine their energies and how stress is distributed in them. For each state a critical value of $se$ is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has two-fold symmetry.
4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to the one published in PRL