Experimental study of shape transitions and energy scaling in thin non-euclidean plates

Yael Klein, Shankar Venkataramani, Eran Sharon

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Abstract

We present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, K tar. We vary the disks' thickness t0 and measure the dependence of configurations, surface curvature, and energy content on t 0. For Ktar<0, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as t0→0, and to a slow decay of both bending and stretching energies. Both vary like t02, compared with t03 of the bending energy in disks with Ktar>0.

Original languageEnglish (US)
Article number118303
JournalPhysical review letters
Volume106
Issue number11
DOIs
StatePublished - Mar 14 2011

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

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