# Characterization and Theoretical Analysis of the Venus Flytrap Trigger Hair
## 3 Results and Discussion
### Simulation Analysis of the STHCBM with Abaqus  
Although the influence of different variables in the formulas to the sensitivity of the trigger hair has been preliminarily demonstrated by mechanics theory, the specific results, which are closely related to the diverse characteristics of the trigger hair, are still unknown for the design of state-of-the-art sensors. As a result, the specific finite element simulation of the characteristics of the trigger hair, including the elastic modulus, the length and the constriction structure, will be used to further verify the internal biological mechanisms. Figure 5 shows the dimensions of the model's podium and lever. The length and diameter of the podium were \(L_{b}=5\) mm and \(D_{1}=1\) mm, respectively, while those of the lever were \(L_{a}=10\) mm and \(D_{2}=1\) mm. The elastic modulus of the podium was set to \(E_{1}=1\) MPa, where as that of the lever was set to \(E_{2}=10\) MPa. Both parts had a density of 1 g/cm\({}^{3}\), and Poisson's ratio was set as v = 0.3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbols** & **Meanings** & **Symbols** & **Meanings** \\ \hline \(w\) & Deflection & \(I_{1}\) & Inertia moment of podium \\ \(w_{a}\) & Lever deflection & \(I_{2}\) & inertia moment of lever \\ \(w_{b}\) & Podium deflection & \(K\) & Elastic coefficient \\ \(\Phi\) & Maximum deflection & \(\sigma\) & Strain \\ \(E_{1}\) & Elastic modulus of podium & \(K_{\sigma}\) & Stress amplification factor \\ \(E_{2}\) & Elastic modulus of lever & \(l\) & Whole length \\ \(L_{a}\) & Lever length & \(\Lambda\) & Flexibility or slenderness ratio \\ \(L_{b}\) & Podium length & \(\mu\) & Length factor \\ \(D_{1}\) & Diameter of podium & \(\sigma_{\sigma}\) & Critical strain \\ \(D_{2}\) & Diameter of lever & \(F_{\sigma}\) & Critical strain \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The meaning of the major symbols in formulas. Figure 5: Pre-processing of finite element analysis of the cantilever beam: (a) setting of boundary conditions and loading of loads for cantilever beams; (b) the division of finite element mesh. A concentrated force of F = 0.0001 N was applied to the tip of the lever, and the bottom of the podium was completely fixed. Then, the mesh size was 0.05 mm at the podium and 0.1 mm at the lever. The neutral axis algorithm was adopted, and the element type was C3D20R. The field output parameters of the simulation results were displacement, stress and strain. According to the theoretical analysis of the previous mathematical model, the results indicated that the main factors affecting the mechanical properties of trigger hair are the ratio of elastic modulus (\(E_{2}/E_{1}\)) and the length ratio of lever to podium (\(L_{a}/L_{b}\)). Therefore, the influences of material parameters and geometric parameters on the simulation results are discussed. Firstly, to examine the impact of material parameters on the mechanical properties of cantilever beam structures, we held constant the geometric parameters of the model and varied the elastic modulus ratio between the lever and podium (\(E_{2}/E_{1}\)). The different material parameter settings are as shown in Table 3.  
It can be seen from Figure 6a that the deflection of the STHCBM occurs at the tip of the lever. In addition, the simulation results show that the deflections of homogeneous STHCBM (\(E_{1}\) = \(E_{2}\) = 1 MPa) and heterogeneous STHCBM (\(E_{1}\) = 1 MPa, \(E_{2}\) = 10 MPa) are 2.293 and 1.671, respectively. Based on Equation (10), the deflection curves of STHCBM under the same force under different \(E_{1}\) and \(E_{2}\) are as shown in Figure 6b,c. The simulation results were marked in the form of scatter points and the theoretical curve is consistent with the simulation results. When the elastic modulus of the podium (\(E_{1}\) = 1 MPa) was fixed, the larger the elastic modulus of the lever (\(E_{2}\)) was, the smaller the deflection of the STHCBM was. When the ratio of \(E_{2}/E_{1}\) was greater than 100, the deflection of the STHCBM was basically constant under the same force.