# Design and Mechanical Properties of Negative Poisson's Ratio Structure-Based Topology Optimization
## 5 Conclusions  
This article suggests modifying the optimization parameters in topology optimization to regulate the final structure, ensuring that it has a negative Poisson's ratio. The mechanical properties of the structure were analyzed using theoretical, quasi-static compression, and finite element analyses. Following verification of the finite element model, numerical simulations examined the size of the concave beetle-inspired structure, including dimensions a, b, c, and h and angles \(\alpha\) and \(\gamma\).  
Based on the results, increasing the size of a moderately reduced the specific energy absorption of the concave structure, exhibiting a linear relationship. The sizes of b and c nonlinearly impacted the specific energy absorption of the concave structure, with increasing b and c initially boosting and then lowering the specific energy absorption. Overall, the specific energy absorption of the structure fluctuated and decreased with increasing h, while \(\alpha\) and \(\gamma\) values exerted a significant impact on the specific energy absorption of the structure. The results indicate that selecting structural dimensions considerably affects the specific energy absorption characteristics of the structure, and optimizing the structure's design can enhance the energy absorption performance by up to 40% compared to the suboptimal case.  
Methodology, M.L.; software, M.L.; validation, D.Q. and M.L.; formal analysis, D.Q.; writing--original draft preparation, M.L.; writing--review and editing, D.Q.; visualization, T.W.; supervision, D.Q.; project administration, J.C. and H.W.; funding acquisition, D.Q. All authors have read and agreed to the published version of this manuscript. This work was supported by the Nature Science Foundation of China under Grant 51705468 and the Key Technologies Research and Development Program under Grant 2018 YFB0106204.  
**Institutional Review Board Statement:** Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\alpha\) & \(\pi\)/8 & \(\pi\)/6 & \(\pi\)/4 & \(\pi\)/4 & \(\pi\)/4 \\ \hline \(\gamma\) & \(\pi\)/4 & \(\pi\)/4 & \(\pi\)/4 & \(\pi\)/6 & \(\pi\)/8 \\ a & 8 & 8 & 8 & 8 & 8 \\ b & 5 & 5 & 5 & 5 & 5 \\ c & 5 & 5 & 5 & 5 & 5 \\ h & 5 & 5 & 5 & 5 & 5 \\ Mass (g) & 52.5 & 53.5 & 55.3 & 55.3 & 55.3 \\ Internal energy (mJ) & 114,771 & 119,584 & 130,221 & 103,603 & 119,691 \\ Specific energy & 2.186 & 2.235 & 2.355 & 1.873 & 2.164 \\ absorption (kJ/kg) & 2.186 & 2.235 & 2.355 & 1.873 & 2.164 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Numerical results for specimens with different sizes of \(\alpha\) and \(\gamma\).  
Figure 21: (**a**) Effect of different \(\alpha\) and \(\gamma\) values on energy. (**b**) Effect of different \(\alpha\) and \(\gamma\) values on specific absorption energy.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of this study; in the collection, analyses, or interpretation of data; in the writing of this manuscript; or in the decision to publish the results.