Fig. 1. Typical pyramid kirigami structure: (a) Pyramid structure with number of edges N = 4 and number of modules n = 3; (b) pyramid model produces vertical deformation under the action of vertical tension F.

Fig. 2. “Beam model” consisting of “beam elements”: (a) Simplified “beam model” of a deformed area of the pyramid structure; (b) “beam element” consisting of cantilever beams.

Fig. 3. Theoretical curve of cantilever beam compared with the approximate theoretical curve of small deflection based on Eq. (1) and (2).

Fig. 4. Verify the relationship between elastic coefficient and structural parameters through FEM simulation and theoretical calculation: (a)−(c) The elastic coefficientK varies linearly with the beam width w, the cube of thickness t, and the number of sides N; (d) take different values b to verify the relationship between the elastic coefficient K and the number of modules n. The points are simulation values, and the dotted lines are calculated values.

Fig. 5. The K and D_T formulas (11) and (14) are verified experimentally: (a) Experimental picture; (b) the experimental data of the quadrangular pyramid structure, the points are the measurement results, the red dotted line is the linear region fitting result, and the black dotted line is the calculated linear threshold; (c) laser-driven deformation of graphene kirigami springs published in Nature^[1].

Fig. 6. Transverse strain of a module: (a) Experimental diagram of module deformation; (b) simple geometric relationship of deformation of a single module.

Fig. 7. Influence of different module cut length L on transverse strain .