TY - JOUR
T1 - Experimental study of shape transitions and energy scaling in thin non-euclidean plates
AU - Klein, Yael
AU - Venkataramani, Shankar
AU - Sharon, Eran
PY - 2011/3/14
Y1 - 2011/3/14
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79952605386&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.106.118303
DO - 10.1103/PhysRevLett.106.118303
M3 - Article
AN - SCOPUS:79952605386
SN - 0031-9007
VL - 106
JO - Physical Review Letters
JF - Physical Review Letters
IS - 11
M1 - 118303
ER -