## 5 Conclusions and Discussions  
Novel hybrid metastructures consisting of an auxetic metal lattice honeycomb and ceramic matrices are designed and fabricated for improving the specific energy absorption and dynamic protection performances of brittle ceramic materials. Lateral constrained compression experiments are performed for verification. Experimental and numerical results show that when the external re-entrant auxetic honeycomb is subjected to compression, uniaxial compression loading along the vertical direction can be converted into both vertical and horizontal compression loading within the infilled ceramic matrix, thus can greatly increase the compressive and impact mechanical performances of single phase infilled ceramic materials. The proposed metal-ceramic hybrid metastructures can provide mechanical advantages of synergistic effects between the ceramics matrix and the metal honeycombs through the phase boundary interaction so that ceramics and metals have better deformation compatibility.  
Based on DIC deformation field analysis and thde in-situ quasi-static compression experiment, it was found that infilled ceramic matrix within the re-entrant hexagonal metal honeycomb structure can effectively reduce stress concentration. A benefit from the negative Poisson's ratio effect and phase boundary metal-ceramic interaction, the outer metal honeycomb can impede crack propagation within infilled ceramic during the compression process. Afterwards, dynamic Hopkinson impact experiments were performed on the single-phase unit cell and the metal-ceramic hybrid honeycomb structure, and it was shown that under the same impact loading conditions, the impact protection performances of the ceramic filled auxetic re-entrant honeycomb was better than that of the ceramic filled ordinary honeycomb structure. Such a protection effect is particularly more remarkable at a higher impact speed. It can also be seen from the experimental results that the unconstrained interface of ceramics is quite vulnerable to impact. Therefore, the hybrid design method of strength and toughness will be more advantageous if 3D auxetic structures are employed as the metal lattice in the hybrid material. Recent studies have shown that the impact resistance of lattice structures is related to impact speed [30]. Our study found that the impact resistances are related to both loading speed and unit cell lattice geometrical configurations. Single ceramic material is superior to the metal-ceramic hybrid structure in terms of dynamic impact energy absorption in Hopkinson tests, respectively. Such dynamic experimental results are quite different from static compression loading results. Such abnormal phenomenon and underlying physical mechanisms will be further studied in the future.  
[PERSON] contributed to the method of synergistic design of strength and toughness, and he wrote the main manuscript; [PERSON] performed the metal and ceramic manufacturing; [PERSON] and [PERSON] contributed to the compress experiment and the Hopkinson bar experiment; [PERSON] and [PERSON] contributed to the data analyses and FEM study in this paper; [PERSON] and [PERSON] supervised the experiments. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (Grant No.: 52005504 and 11972081).  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The work was conducted at the National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1 (A).  
The authors declare that they have no conflict of interests.