Fig. 3: Metamaterial consisting of planetary gear systems.

a, Metacell, a planetary gear system. The origin (O) of the coordinates x,y is the centre of the sun gear (green). A_i and B_i denote the centres of planetary gears (grey). Their revolution angle denotes θ_pr = ∠YOA₁. The case A₁A₂ ⊥ B₁B₂ is drawn here, and thus θ_pr = ∠XOB₁ = ∠YOA₁. A transmission gear (yellow) connects to the sun gear through a shaft. b, Typical compressive and tensile deformation of a metacell. c, Macro metallic metamaterial architecture. d, Macro polymer metamaterial with 6 × 6 metacells. e, Micro polymer metamaterial with 3 × 4 metacells. f, Micrograph for the metamaterial in e. Specimens in d and e are fabricated with integrated manufacturing. g, Measured strain–stress curves. h,i, Measured and simulated Young’s moduli under compression and tensile deformation, E_c and E_t, of the macro metallic (h) and micro (i) specimens. Results of the macro polymer sample are shown in Supplementary Fig. 12b. The error bars and the average values in h and i are evaluated by choosing different intervals near the maximum strain along the curve in g.