Fig. 2: Conceptual design of synthetic nano-kirigami structure with bi-directional deformations.

a Schematic of the upward deformation with a bilayer prestress model³², in which the residual stress distribution in the cantilever is different (causing the top and bottom of the cantilever to be contracted and stretched, respectively), the cantilever will deform upward due to the stress difference existed in the bilayer areas when one side is fixed (as marked by the red region). b Schematic of downward deformation of the cantilever under a vertically downward pressure³⁶. c, d Simulated out-of-plane upward and downward deformation displacements of the synthetic nano-kirigami (with a spiral angle of 360°) under prestress and pressure, respectively. Left insets: The corresponding calculated deformability (\(\xi\)) versus the applied prestress and pressure. Here \(\xi=D/d\), where D and d represent the deformation displacement and structural span width, respectively. Simulated stress (e, Von Mises stress) and strain (f) distributions of the dynamically deformed synthetic nano-kirigami structure (with a spiral angle of 270°).