Conical defects in growing sheets

Details Conical defects in growing sheets Conical defects in growing sheets

2008-07-11

arxiv.org/abs/0807.1814v2

Phys. Rev. Lett. 101 (15), 156104 (2008)

Physics

Condensed Matter

Other Condensed Matter

4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to the one published in PRL

Scientific paper

10.1103/PhysRevLett.101.156104

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.

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