Fig. 4: The multidirectional axial deformation and mechanical characterization of quadrilateral ring metamaterials.

a The prototype snapshots of designed quadrilateral rings with CII and R functional groups at initial stable state, the final states with axial deformation with Poisson’s ratio v = 0, and auxetic deformation with v = −1. The geometry of quadrilateral ring metamaterials is fixed by 3D-printed plastic structural supports, see detail in Supplementary Fig. 27. The green arrows in snapshots point out the forced direction. b The stress–strain curves and c Comparison of stiffness modulus of the quadrilateral ring constructed by CI, CII, CIII, and R functional groups under multidirectional axial deformation. The solid lines and hollow dots in (b) represent theoretical results and experimental results, respectively. Source data in (b) are provided as a Source Data file.