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 t₀ 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 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 K_tar>0.