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Phys Rev Lett. 2008 Oct 10;101(15):156104. Epub 2008 Oct 10.

Conical defects in growing sheets.

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1
Laboratoire de Physique Statistique de l'Ecole Normale Supérieure (UMR 8550), associé aux Universités Paris 6 et Paris 7 et au CNRS, 24, rue Lhomond, 75005 Paris, France.

Abstract

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle phi(e) at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if phi(e)<or=0, the disc can fold into one of a discrete infinite number of states if phi(e)>0. 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 phi(e) is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.

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