# Study of In-Plane Mechanical Properties of Novel Ellipse-Based Chiral Honeycomb Structure
## 4 Conclusions  
In this paper, we designed and gave the analytical solutions of in-plane [PERSON]'s ratio and [PERSON]'s modulus of E-antitet by theoretical derivations and verified them by numerical solutions of FEM simulations and experimental tests of 3D printed samples. The results verified the correctness of this theoretical model and numerical simulations. The trends of [PERSON]'s ratio and [PERSON]'s modulus of E-antitet in different directions are discussed by adjusting five different parameters, and comparisons with the conventional antitet structures are given. The results show that E-antitet can achieve a smaller [PERSON]'s ratio and larger Young's modulus in a certain direction, and the range of the difference between [PERSON]'s ratio and [PERSON]'s modulus in that direction depends on the radius of the node ring of the antitet. A wide range of adjustment of the overall [PERSON]'s ratio and Young's modulus can be achieved by adjusting the long and short axes \(a\) and \(b\) of the elliptical and the ligament lengths \(l_{x}\) and \(l_{y}\) in both directions.  
It should be noted that the in-plane mechanical properties of E-antitet are studied under the conditions of small strain and can only be used for the linear elasticity. The in-plane mechanical properties at large strains still need further study in future work. In addition, although E-antitet proposed in this paper shows better properties than antitet, it still does not completely solve the disadvantage of the weak load-bearing capacity of honeycomb structures. We hope that this problem can be completely improved in the future research.  
Conceptualization, W.X.; Data curation, W.W., J.W. and H.H.; Formal analysis, J.W.; Investigation, W.W.; Methodology, W.W. and W.X.; Software, J.W.; Writing--review & editing, X.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Natural Science Foundation of China (Nos. 11302135 and 11672007), Suqian Sci&Tech Program (No. K202124). Not applicable. The authors gratefully acknowledge the financial supports. The authors declare no conflict of interest.  
Figure 9: Trends of Poisson’s ratio and Young’s modulus of E-antitet at different \(\gamma\): Comparison of the results of analytical and numerical solutions of E-antitet with antitet-1 and antitet-2. (**a**) [PERSON]’s ratio and (**b**) [PERSON]’s modulus.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{\(\mathbf{\gamma}\)} & \multicolumn{6}{c}{**Theory**} & \multicolumn{6}{c}{**FEM**} \\ \cline{3-10}  & & \(\mathbf{v_{xy}}\) & \(\mathbf{v_{yx}}\) & \(\mathbf{E_{x}}\) (MPa) & \(\mathbf{E_{y}}\) (MPa) & \(\mathbf{v_{xy}}\) & \(\mathbf{v_{yx}}\) & \(\mathbf{E_{x}}\) (MPa) & \(\mathbf{E_{y}}\) (MPa) \\ \hline \multirow{4}{*}{**Type**} & 0.8 & \(-1.00\) & \(-1.00\) & 28.25 & 28.25 & \(-0.89\) & \(-0.89\) & 29.33 & 29.33 \\  & 0.9 & \(-1.00\) & \(-1.00\) & 28.25 & 28.25 & \(-0.89\) & \(-0.89\) & 29.27 & 29.27 \\  & 1 & \(-1.00\) & \(-1.00\) & 28.25 & 28.25 & \(-0.89\) & \(-0.89\) & 29.28 & 29.28 \\  & 1.1 & \(-1.00\) & \(-1.00\) & 28.25 & 28.25 & \(-0.89\) & \(-0.89\) & 29.26 & 29.26 \\  & 1.2 & \(-1.00\) & \(-1.00\) & 28.25 & 28.25 & \(-0.89\) & \(-0.89\) & 29.36 & 29.36 \\ \hline \multirow{4}{*}{**Type**} & 0.8 & \(-0.43\) & \(-2.33\) & 6.73 & 36.66 & \(-0.40\) & \(-2.09\) & 6.35 & 35.64 \\  & 0.9 & \(-0.43\) & \(-2.33\) & 6.73 & 36.66 & \(-0.39\) & \(-2.09\) & 6.35 & 35.62 \\  & 1 & \(-0.43\) & \(-2.33\) & 6.73 & 36.66 & \(-0.39\) & \(-2.09\) & 6.35 & 35.64 \\  & 1.1 & \(-0.43\) & \(-2.33\) & 6.73 & 36.66 & \(-0.39\) & \(-2.10\) & 6.36 & 35.66 \\  & 1.2 & \(-0.43\) & \(-2.33\) & 6.73 & 36.66 & \(-0.39\) & \(-2.10\) & 6.36 & 35.68 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Detailed results of [PERSON]’s ratio and [PERSON]’s modulus of E-antitet at different \(\gamma\).