## 3 Results and Discussion
### Three-Point Bending Properties  
During the three-point bending tests, the two ends of the bio-inspired structures (BSs) were fixed, and a displacement-controlled loading was applied to the middle portion. The loading was performed in 10 steps with a step length of 0.1 mm. Figure 7 presents the finite element model used in the three-point bending tests, which employed the shell 181 cell type and refined the contact area of the mesh. Figure 8a illustrates the comparison between experimental results and the simulation of BS-7. The bending load of the three samples of BS-7 and the theoretical model exhibit a similar overall trend, rising with the increase in displacement, declining briefly when the displacement is 7-9 mm, and then increasing gradually. When the bending load of the BS-7 structure reaches its maximum, it starts to drop sharply, and damage occurs. Figure 8b illustrates the bending load displacement simulation curve of different BSs. The bending load of all BSs structures increases with the increase in displacement, and the bending loads reach the maximum when the displacement is 32-35 mm, and then starts to drop sharply. Evidently, BS-1 and BS-2 are damaged first, and the maximum bending load is small. Therefore, the three-point bending characteristics are also poor compared with other BSs. The maximum bending load of BS-4, BS-6, and BS-7 is large, and three-point bending characteristics are good. Figure 8c clearly demonstrates the bending strength of different BSs. The minimum bending strength of BS-2 is 3684.3 N, and the maximum bending strength of BS-4 is 5339.8 N. The bending strength of BS-3 and BS-5 is close to that of BS-1, which increased by 5.3% and 8%, respectively. Moreover, the internal structure of BS-3 is a single quadrilateral, the internal structure of BS-5 is a single pentagon, and there is no polygon in BS-1, indicating that the addition of the polygon structure can improve the bending strength of thin tubes. Compared with BS-4, the bending strength of BS-3 is lower than that of BS-4, and the bending strength of BS-4 is 33.8% higher than that of BS-3. The internal structure of BS-3 is a single quadrangle, while that of BS-4 is two quadrangles. The bending strength of BS-6 is \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Simulation/Test Values** & \begin{tabular}{c} **Mass** \\ **(g)** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum Torsional** \\ **Load (N\(\cdot\)m)** \\ \end{tabular} &
\begin{tabular}{c} **LWN-T** \\ **(N\(\cdot\)m/g)** \\ \end{tabular} \\ \hline BS-1 & Simulation values & 103.42 & 106.8 & 1.03 \\ BS-2 & Simulation values & 103.42 & 63.71 & 0.62 \\ BS-3 & Simulation values & 103.42 & 107.35 & 1.04 \\ BS-4 & Simulation values & 103.42 & 126.64 & 1.22 \\ BS-5 & Simulation values & 103.42 & 109.16 & 1.06 \\ BS-6 & Simulation values & 103.42 & 122.42 & 1.18 \\  & Test sample \#1 & 103.38 & 129.76 & 1.26 \\ BS-7 & Test sample \#2 & 103.46 & 128.98 & 1.25 \\  & Test sample \#3 & 103.45 & 129.01 & 1.25 \\  & Simulation values & 103.42 & 124.02 & 1.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of experimental and simulated torsion data. 25.1% higher than that of BS-5. The internal structure of BS-6 is two hexagons, while the internal structure of BS-5 is a single hexagon. According to [PERSON] et al. [11], the difference in bending strength between BS-6 and BS-5 can be attributed to the impact of fractal configuration and geometric shape on material properties. The study demonstrated that fractal configuration and sub-hexagon length have a strong influence on energy absorption, while [PERSON] et al. [40] and [PERSON] et al. [41] found that hexagonal honeycomb structures have stronger bending performance. Therefore, BS-6 adopts an internal structure consisting of two hexagons, which is superior to BS-5's single hexagon structure under the same conditions.