# Characterization and Theoretical Analysis of the Venus Flytrap Trigger Hair
## 3 Results and Discussion
### The Characteristics of the Venus Flytrap Trigger Hair
The Piuma Nano-indenter equipped with a new type of fiber optic interferometry cantilevered spherical probe was set to the Hertzian model and its Poisson's ratio was set to 0.5. Finally, the sample was placed on the sample stage for the nanoindentation experiment. Figure 2b displays the image of the Venus flytrap trigger hair under the nano-indenter. As Figure 2c shows that, under the same indentation, the hair lever obtained a higher load than the basal podium, which clearly shows the elastic modulus of the lever is much higher than that of the podium. With the help of professional data analysis software (Optics11 Date Viewer V2.5.0), the elastic modulus of the basal podium and hair lever was determined to be 138.167 Kpa and 18.167 Mpa, respectively (Figure 2d). Obviously, the elastic modulus of the basal podium is significantly less than that of the trigger hair lever. This means that the trigger hair of the Venus flytrap is a rigid-flexible coupled structure, rather than the traditional homogeneous cantilever beam structure. This may be one of the important factors that enable the trigger hairs of the Venus flytrap to achieve high sensitivity. The influence of the elastic modulus difference between two materials on trigger hair deformation will be analyzed in the next study. Moreover, in order  
Figure 2: Biomechanical properties of Venus flytrap: (**a**) the image of the Venus flytrap trigger hair fixed with glue; (**b**) image of Venus flytrap trigger hair observed under nano-indenter; (**c**) load–displacement curve at various indentation depths; (**d**) elastic modulus of hair lever (red) and basal podium (green), respectively. to further carry out theoretical analysis, the structural parameters of the basal podium and the trigger hair lever are summarized in Table 1.  
The biological studies have revealed that Venus flytrap trigger hair is a typical composite beam made up of two materials with different mechanical properties [21; 22]. Based on the relevant theories of solids mechanics [23], when the load is applied at the tip of the distal lever (the right end in Figure 3), the deflection angle \(\theta\) of the cantilever beam can be expressed as:  
\[\theta=\int\frac{d^{2}w}{dx^{2}}=\int\frac{M(x)}{EI}dx \tag{1}\]  
Here, \(E\) is the elastic modulus of material, and \(I\) is the moment of inertia of the cantilever beam cross section to neutral axis. \(\mathbf{M(\alpha)}\) is the bending moment in different areas of the beam. Then, the deflection \(w\) of the beam can be expressed as:  
\[w=\int\theta dx \tag{2}\]  
Combined Equations (1) and (2), the \(w\) is further given by:  
\[w=\int\frac{M(x)}{EI}dx+C_{1}x+C_{2} \tag{3}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value (\(\mathbf{\mu}\))** \\ \hline Length of hair lever & \(L_{a}\) & \(3297.32\pm 53.58\) \\ \hline Length of basal podium & \(L_{b}\) & \(114.05\pm 35.43\) \\ \hline Diameter of hair lever & \(D_{2}\) & \(180.79\pm 13.03\) \\ \hline Diameter of basal podium & \(D_{1}\) & \(183.45\pm 5.33\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Structural parameters of the basal podium and hair lever. Figure 3: The model of the trigger hair of Venus flytrap: (**a**) schematic diagram of STHCBM without notch structure; (**b**) schematic diagram of STHCBM with notch structure. Firstly, for the composite beam, the basal podium is regarded as a rigid body, the \(w_{a}\) caused by the deformation of the hair can be given by:  
\[w_{a}=\theta_{b}\cdot L_{a}+\omega_{a_{0}} \tag{4}\]  
\[w_{a}=\frac{FL_{b}^{2}L_{a}}{2E_{1}I}+\frac{FL_{a}^{2}L_{b}}{E_{1}I}+\frac{FI_{a }^{3}}{3E_{2}I} \tag{5}\]  
Here, the \(E_{1}\) and \(E_{2}\) are the elastic modulus of the hair's podium and lever, respectively. \(L_{b}\) and \(L_{a}\) are their respective lengths.