Fig. 1. One-dimensional multi-stable metamaterial unit cell

Fig. 2. One-dimensional multi-stable metamaterial in tensile stable state and compressive stable state

Fig. 3. Three-dimensional multi-stable metamaterial unit cell in tensile stable state and compressive stable state

Fig. 4. Irreducible Brillouin Zones of the three-dimensional structure

Fig. 5. Energy band structure analysis. （a） In-plane band structure of the tensile stable state； （b） in-plane band structure of the compressive stable state

Fig. 6. Modes corresponding to edge frequencies of the first bandgap in the tensile stable state and compressive stable state

Fig. 7. Frequency response analysis. （a） Frequency response calculation model； （b） frequency response curve in the tensile stable state； （c） frequency response curve in the compressive stable state

Fig. 8. Modes corresponding to the horizontal dispersion curve of the third bandgap in the tensile stable state and compressive stable state

Fig. 9. Energy band structure analysis. （a）In-plane band structure of the three-dimensional tensile stable state； （b）in-plane band structure of the three-dimensional compressive stable state

Fig. 10. Frequency response analysis of three-dimensional tensile stable and three-dimensional compressive stable metamaterial

Fig. 11. Frequency response calculation of three-dimensional tensile stable state and three-dimensional compressive stable state