Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates

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 t(0) and measure the dependence of configurations, surface curvature, and energy content on t(0). For K(tar)<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 t(0)→0, and to a slow decay of both bending and stretching energies. Both vary like t(0)(2), compared with t(0)(3) of the bending energy in disks with K(tar)>0.