Year: 2008
Type: article
Abstract: A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle ${\ensuremath{\varphi}}_{e}$ at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if ${\ensuremath{\varphi}}_{e}\ensuremath{\le}0$, the disc can fold into one of a discrete infinite number of states if ${\ensuremath{\varphi}}_{e}>0$. 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 ${\ensuremath{\varphi}}_{e}$ is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has twofold symmetry.
Source: Physical Review Letters
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2042806071