Fig. 3: Mining extreme Young’s modulus and Poisson’s ratio from the resulting database composed of 1,846,182 truss metamaterials.

A The range of effective Young’s moduli E_x and E_y along the horizontal and vertical directions is visualized with extreme examples marked. Compared with the reported range composed of classic metamaterials (triangle scatters), the number of new metamaterials with superior effective Young’s moduli (star scatters) is up to 2939. The reported range refers to the properties of the classic metamaterials^{37,38,40,41,42,43,44,45} (Fig.2, insets c1 ~ c12), which are generated by the design method and included in the database²². B The range of Poisson’s ratios is visualized with extreme examples highlighted. ν_xy and ν_yx characterize the lateral contraction for loading along the x and y directions, respectively. The scales of the scatter represent the magnitude of Poisson’s ratios. C Mechanism for enhancing effective Young’s moduli. The diamond with reinforced struts presents the stretching-dominated behavior, which contributes to the superior effective Young’s moduli. D Mechanism for extreme Poisson’s ratio. The larger displacements of the struts on either side of the virtual fulcrum are responsible for the extreme Poisson’s ratio. E1 ~ E4 Trade-off bound and extreme examples for different couples of mechanical properties. Extreme modulus and Poisson’s ratio are inherent contradictions. The generated database can effectively mine the bounds of coupling properties. Source data are provided in the Source Data file.