## 5 Discussions
Figure 19 shows that values of the maximum stress triaxiality and equivalent plastic strains of the three specimens with different chamfering radii were close to each other, indicating a minor effect of chamfering radius on the ductility of the specimens, as shown in Figure 21.  
Figure 14: Effect of concave angle on load–displacement curves. Figure 15: Effect of concave angle on stress triaxiality with (**a**) H40A75R0.5 (**b**) H40A80R0.5 (**c**) H40A85R0.5. Figure 16: Effect of concave angle on equivalent plastic strain with (**a**) H40A75R0.5 (**b**) H40A80R0.5 and (**c**) H40A85R0.5. Figure 9:0 Effect of concave angle on damage index with (**a**) H40A75R0.5 (**b**) H40A80R0.5 and (**c**) H40A85R0.5. In the design of re-entrant honeycomb structures, the behavior could also be affected by the proportion of solid area. In the original design, the total length of the specimen was 256 mm. The length of the perforated area was a fixed value of 76 mm, so the length of the solid area \(l_{\mathrm{s}}\) at both ends was 90 mm. The two long un-perforated edges were expected to achieve enough holding forces at the chucks. This length was mainly to ensure that the MTS machine chucks had enough clamping space. Nevertheless, although this paper focused on the mechanical performance of the perforated area, the large solid area may have affected the mechanical properties and Poisson's ratios of the specimens. In order to evaluate this effect, two additional FE models were established according to Specim H40A85R0.5, with different lengths of solid area \(l_{\mathrm{s}}\) of 20 mm and 50 mm, to compare with the original lengths of 90 mm, as shown in Figure 9:1 Among the three models, the ratio of the perforated area to the surface area of the specimen was 29.7%, 43.2% and 65.5%, respectively. Explicit integration schemes were employed for these models with the same boundary conditions. Figure 9:2 Effect of chamfering radius on stress triaxiality with (**a**) H40A85R0, (**b**) H40A85R0.5 and (**c**) H40A85R1. Figure 9:3 Effect of chamfering radius on load–displacement curves. According to the load-displacement curves shown in Figure 23a, the curves matched well before reaching the failure point and were similar in their failure process, which indicated that the bearing capacity and ductility of perforated area was almost unaffected by the length of solid area \(l_{\text{s}}\). Figure 23b shows the fracture model with almost the same damage and cracking behaviors. On the other hand, the curves of Poisson's ratio at the convex and concave points, were obtained from the numerical results, shown in Figure 9:4 Generally, the specimens with a small solid region showed better negative Poisson's ratio performance. The maximum negative Poisson's ratio of the model with \(l_{\text{s}}\) of 20 mm and 50 mm was \(-0.3\), while the maximum negative Poisson's ratio of the original model was \(-0.2\). After the strain exceeded 0.15, the negative Poisson's ratio of the model with a solid area length of 20 mm and 50 mm gradually approached 0.1, while the original model gradually approached 0.2. The Poisson's  
Figure 9:5 Effect of chamfering radius on damage index with **(a)** H40A85R0, **(b)** H40A85R0.5 and (c) H40A85R1. Figure 9:6 Effect of chamfering radius on equivalent plastic strain with **(a)** H40A85R0, **(b)** H40A85R0.5 and (c) H40A85R1. ratio of the model with a length of 20 mm was smaller than that of the model of 50 mm in general when the strain exceeded 0.2. Figure 9:7 (**a**) Load–displacement curves and (**b**) failure modes of specimens with different solid areas. Figure 9:8 H40A85R0.5 specimens with different lengths of solid area. The reason for the above result is easy to understand. The Poisson's ratio of the steel in the solid region was 0.5 in the plastic range. The unperforated edges had a positive Poisson's ratio of 0.5, which could restrain lateral expansion of the perforated part. Therefore, a shorter length of the solid area led to better auxetic performance.