## 5 Discussions  
To clarify the mechanisms of influence of each parameter on the elastoplastic performance of specimens, numerical analyses were conducted using the aforementioned FE models. Seven specimens with the same configurations as those use in the the experiments were constructed and compared with each other, including the two specimens failing prematurely. Load-displacement curves of the 2D re-entrant honeycomb specimens with different hole ratios are compared in Figure 9, and indicated that the three specimens had almost the same load-displacement curves. The specimens with different hole ratios were designed with the same width for each edge of the re-entrant honeycomb unit, meaning that the strength and stiffness values of the three specimens were almost the same. To investigate the effect of hole ratio on the stress and strain conditions of specimens, equivalent plastic strain, stress triaxiality, and damage index contour plots at an average strain of about 10% were compared as shown in Figures 10-12, respectively. Figure 10 shows that values of maximum stress triaxiality of the three specimens with different hole ratios were close to each other, but the maximum equivalent plastic strain of Specim H50A85R0.5 is much larger than that of the other two specimens, leading to early crack initiation of the specimen. Figure 8: Comparison of failure modes with **(a)** H40A85R0.5, **(b)** H50A85R0.5, **(c)** H40A80R0.5, **(d)** H40A85R0 and **(e)** H40A85R1. Figure 9: Effect of hole ratio on load–displacement curves. The Poisson's ratio versus average strain curves are given in Figure 13, where the average strain is defined as the ratio of the relative vertical displacement of the perforated segment to the its length, and the Poisson's ratios were calculated from the horizontal and vertical average strain data. Horizontal displacement data of the two typical points shown in Figure 13, i.e., convex point (blue) and concave point (red), were obtained from the numerical results. Comparing Figure 13a-c, it can be seen that specimens with different hole ratios had a similar tendency. For Specimens H30A85R0.5, H40A85R0.5, and H50A85R0.5, the Poisson's ratio was positive at the initial loading stage, and then changed to negative quickly before 0.15%. The Poisson's ratios changed to positive values with an increasing vertical average strain, and achieved the maximum value. The Poisson's ratio then decreased while still maintaining a positive value. Generally, the hole ratio had some effect on variation of the Poisson's ratio, especially for Specim H30A85R0.5, which was quite different from the other two specimens. Figure 11: Effect of hole ratio on equivalent plastic strain with **(a)** H30A85R0.5 **(b)** H40A85R0.5 and **(c)** H50A85R0.5. Figure 10: Effect of hole ratio on stress triaxiality with **(a)** H30A85R0.5 **(b)** H40A85R0.5 and **(c)** H50A85R0.5. Figure 12: Effect of hole ratio on damage index with (**a**) H30A85R0.5 (**b**) H40A85R0.5 and (**c**) H50A85R0.5. Figure 13: Effect of design parameters on Poisson’s ratio. Comparing Figure 13b,d,e, it can be seen that the concave angle had a great effect on the Poisson's ratio. For Specim H40A75R0.5, the Poisson's ratio ranged from about \(-0.5\) to \(0\), and was almost always below \(0\) throughout the whole loading history until rupture. However, the Poisson's ratio ranged from about \(-0.2\) to \(0.2\) and \(-0.2\) to \(0.3\) for Specimens H40A80R0.5 and H40A85R0.5, respectively. As the concave angle decreased, the Poisson's ratio tended to decrease, and it is expected that an angle below \(75^{\circ}\) can ensure that the Poisson's ratio of a specimen will remain negative throughout the whole loading process. This conclusion was inferred from the geometric configurations of the specimens. The concave edges of each cell were gradually straightened in the process of stretching, so that the opening areas showed a trend of changing from concave hexagons to rectangles. In this process, expansion perpendicular to the stretching direction gradually occurred.