# Design and Mechanical Properties of Negative Poisson's Ratio Structure-Based Topology Optimization
## 4 Crasworthiness Analysis of the Concave Beetle-Shaped Honeycomb Structure
### Influence of Cellular Structural Parameters on Crashworthiness
#### 4.3.2 The Effect of Cellular Oblique Edge b  
The impact performance of the oblique edge of the unit cell was analyzed while keeping the original cell's other structures unchanged. Changes in energy absorption are scrutinized as the parameter \"b\" varied from 4 to 6 mm.  
The specific parameters of the cellular structure, internal energy, and specific energy absorption curve after the impact are shown in Table 7 and Figure 18. As the parameter b increases, it leads to an increase in the specific energy absorption. The specific energy absorption reaches its maximum value at b = 4.5 mm and subsequently decreases. Table 7 shows that increasing the parameter \"b\" increases the mass of the structure, and as a result, the internal energy absorbed by the structure also increases monotonically. However, because of the increase in mass, the specific energy absorption of the structure does not increase monotonically but increases first and then decreases. An analysis of Table 7 concludes that the oblique edge \"b\" of the unit cell increases the amount of internal energy absorbed by the structure, and thus, it is a crucial factor in determining the energy absorption of the structure. It is recommended to note the b size selection to achieve optimal energy absorption performance.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**b** & **4** & **4.5** & **5** & **5.5** & **6** \\ \hline a & 8 & 8 & 8 & 8 & 8 \\ c & 5 & 5 & 5 & 5 & 5 \\ h & 5 & 5 & 5 & 5 & 5 \\ \(\alpha\) & \(\pi/4\) & \(\pi/4\) & \(\pi/4\) & \(\pi/4\) & \(\pi/4\) \\ \(\gamma\) & \(\pi/4\) & \(\pi/4\) & \(\pi/4\) & \(\pi/4\) & \(\pi/4\) \\ Mass (g) & 52.3 & 53.8 & 55.3 & 56.8 & 58.3 \\ Internal energy (mJ) & 122,969 & 127,928 & 130,221 & 133,175 & 135,241 \\ Specific energy & 2.351 & 2.378 & 2.355 & 2.345 & 2.320 \\ absorption (kJ/kg) & & & & & \\ \end{tabular}
\end{table}
Table 7: Numerical results for specimens with different sizes of b.  
Figure 17: (**a**) Effect of different a values on energy. (**b**) Effect of different a values on specific absorption energy.  
4.3.4. The Effect of Cellular Vertical Edge h  
This study analyzed the effect of the vertical edge of the unit cell on impact performance by analyzing the changes in the energy absorption while keeping the original cell's other structures unchanged.  
Table 9 and Figure 20 illustrate the specific parameters of the cellular structure, internal energy, and specific energy absorption under impact. The internal energy of the structure remains relatively stable with minimal change. The specific energy absorption of the structure decreases initially and then increases in irregular fluctuations around 2.3 kJ/kg. The maximum overall specific energy absorption of the structure is attained when \"h\" equals 4 mm. An increase in \"h\" results in an increase in the mass of the entire structure and can cause the internal energy absorbed by the structure to signal a decreasing and then increasing trend, as evident in Table 9.