Fig. 3

Comparisons of the bending stiffness and spring constant enhancement factors (EF). a Comparison of the bending stiffness and areal density of the nanocardboard structure to other plate materials. The nanocardboard bending stiffness is provided as experimental data points and theoretical trend lines, the same as those in Fig. 2. The green square and blue circle data points are for plate-like mechanical metamaterials: ultrathin corrugated alumina²⁸ and inverse-opal alumina shell³⁹. The theoretical stiffness of standard materials, silicon and alumina, are shown as baselines. b Enhancement factor for the bending stiffness of nanocardboard versus the cantilever height for the experimentally used basketweave parameters (l_rect = 50 μm, w_rect = 5 μm, g = 20 μm). c Density and contour plots of the enhancement factor for the spring constant, which considers both shear and bending deformations, versus the plate height and the webbing rectangle length. The plot is based on the analytical model described in the Supplementary Note 5 and assumes a cantilever length L = 9 mm and thickness t = 50 nm. The three open circles indicate the parameters used in experiments. d Same as (c) based on the interpolated results of finite-element simulations. The raw results of finite-element simulations are available in Supplementary Fig. 11c. Error bars are provided as 1 standard deviation for the experimental data points. The data in a and b are the same as Fig. 2c