## 4 Results and Discussion
### Mechanical Tests
The maximum horizontal strain is 8.79%, exhibiting high local strain concentration features. Accordingly, the ceramic infilled matrix with an obvious horizontal strain suddenly falls off, as shown in Figure 3a. Figure 4: Strain contour along horizontal direction of built-in ceramics harvested from DIC measurements (**a–c**) conventional hex (**d–f**) re-entrant hex. (**a,d**) Strain contour at the beginning of compression (the strain of the compress test in vertical direction is 0.5%), (**b,e**) Strain contour at half time of compression failure period (the strain of the compress test in vertical direction is 2.88% for conventional hex and 3.70% for re-entrant hex), (**c,f**) Strain contour at the moment before compression failure (the strain of the compress test in vertical direction is 5.75% for conventional hex and 7.39% for re-entrant hex). Figure 3: (**a**) displacement-load curves of the two hybrid structures in the compression test, (**b**) compressed conventional hex structure after the failure displacement of 2.59 mm (strain of 5.75%), (**c**) compressed re-entrant hex auxetic structure after the failure displacement of 3.33 mm (strain of 7.39%). structure at the same compression loading steps. At the beginning of the compression process, the compress strain along the vertical direction is 0.5%. As shown in Figure 4d, the strain value within the ceramic matrix is low and the strain field is almost evenly distributed. The maximum strain of the built-in ceramic along the horizontal direction is 0.23%, and the strain of most built-in ceramic along the horizontal direction is less than 0.02%. As shown in Figure 4e, the strain value along the vertical direction is 3.70%. Unlike conventional hex, the re-entrant hex does not exhibit a large local horizontal strain concentration band along vertical direction. There are three short stripes with obvious stress concentration near the compression top and bottom boundaries within the re-entrant ceramic matrix. The horizontal strain within these areas is above 0.70%, and the maximum local strain value is 1.97%. At the moment before compression failure, the strain of the compress test along the vertical direction is 7.39%, as shown in Figure 4f. In addition to the original strip areas with an obvious horizontal strain, new short strip areas appear. The strain value within these local strip areas is generally about 1.33%, and the maximum horizontal strain is 2.34%. Due to the limitation of metal materials on horizontal sides, the horizontal strain is also significantly smaller in value than the conventional hexagonal honeycomb. At the same time, due to the influence of the negative Poisson's ratio effect, the vertical strip area with an obvious horizontal strain will not penetrate the whole ceramic from the top to the bottom. In the ceramic-metal hybrid honeycomb structure design, the synergistic effect for improving the energy absorption during the compression process is expected, where interaction between the metal frame and the infilled ceramic matrix will contribute to the deformation modes evolution, failure features, and improvement of damage limits. The energy consumed during the loading process for the ceramic-metal hybrid honeycomb is larger than the sum of each constituent single phase material under compression separately and can be expressed as \(1+1>2\). As shown in Figure 5a,b, the compression displacement-force curve of ceramic-metal hybrid lattice is given. Meanwhile, compression experiments of the single ceramic phase and the single metal phase were also conducted with Instron-5985, and corresponding displacement-force curves are plotted for comparisons. Table 2 shows the details of synergistic effects during the quasi-static compression test, where HAR is the hybrid arithmetic ratio of the arithmetic sum and hybrid structure. Compared with the conventional hexagonal honeycomb structure, the re-entrant hexagonal auxetic structure shows advantages over single ceramic, single metal, and conventional hybrid honeycomb structures.