Characterization and Theoretical Analysis of the Venus Flytrap Trigger Hair

Abstract

The Venus flytrap, which possesses a number of mechano-sensitive trigger hairs, is a typical carnivorous plant that effectively senses and catches insects to survive in nutrient-poor habitats. When insects touch the trigger hairs on a leaf, once they reach the threshold, the Venus flytrap induces an action potential and sharply closes to capture the prey. In this paper, the trigger hairs obtain a special cantilever beam structure with a stiff hair lever and a flexible basal podium, and there is a noticeable notched structure at the basal podium, which differs from a common homogeneous hair. Based on the characteristics of the Venus flytrap trigger hairs, we established a three-dimensional model and conducted theoretical and finite element analysis. The results show that the unique hollow heterogeneous cantilever structure of the Venus flytrap trigger hair can achieve high sensitivity and optimal tactile perception. Overall, the morphology, structure and mechanical characteristics of Venus flytrap trigger hairs were characterized in detail, which may provide a deeper understanding of the trigger hairs’ tactile perception mechanism. And the mechanical simulation and optimization analysis of Venus flytrap trigger hairs had an important theoretical basis and parameter support for the further design of state-of-the-art tactile sensors with high sensitivity inspired by Venus flytrap trigger hairs.

1. Introduction

Typical creatures in nature have evolved to have sophisticated biological mechanoreceptors with excellent performance for the sake of survival and reproduction in the harsh natural environment [1,2,3]. Sophisticated mechanoreceptors are composed of a mechanosensory micro/nano structure with unique physical mechanisms and sensory neurons, and have advantages such as ultrahigh sensitivity, miniaturization, stability and anti-interference, providing a great deal of inspiration for urgently needed mechanosensors that are difficult to obtain through conventional methods [4].

Among these creatures, the Venus flytrap, living in nutrient-deficient bogs, was systematically investigated by Darwin and this plant was considered as “one of the most wonderful in the world”. Mechanoreceptors play a key role in active trapping for the Venus flytrap. The Venus flytrap consists of a modified leaf with two red lobes. Each lobe is edged with needle-like teeth that interlock with those of the other lobe when the trap closes, helping to confine the prey [5]. Three or four mechanical sensory hairs act as the trigger for the trap. It is necessary to stimulate one or more hairs several times to make the trap close [6]. The trigger hair design for the Venus flytrap is similar to the mechanosensors of many arthropods, where a rigid lever amplifies force and concentrates stress in the location of a flexible hair podium where a dendritic tip is located [7,8].

The Venus flytrap is a typical example of an insectivorous plant with an extraordinary tactile sense. Related studies have revealed that deflections of 2.9°, angular velocities of 3.4/s and forces of 29 µN could produce action potential in the trigger hair of the Venus flytrap, and flytraps can detect much smaller torques (160 nN·m) [9]. To clearly verify that the ultra-sensitivity of the trigger hairs is related to the unique characteristics, Yilun Sun and Xing Wang et al. established models based on biology and verified them through finite element methods [10,11]. However, despite a good understanding of the Venus flytrap with respect to the physiology of the snap-trap triggering mechanism [12,13,14], theoretical modeling of the tactile receptor of the Venus flytrap, trigger hair, remains incomplete.

Related studies of the cantilever-based tactile sensor, focusing on the whiskers of mammals and the cilia of arthropods, pay more attention to the homogeneous hair with a smooth structure. As a result, scientific computing methods have hardly been used to bypass the challenges associated with the characterization of Venus flytraps. Here, cantilever beam structure-based models of the sensory trigger hair was developed and its feasibility was verified using the finite element method. To build the models, the morphology and structure of the trigger hair were carefully observed using a Scanning Electron Microscope (SEM). Then, force deflection tests on the top of the hair lever were carried out for investigating the deformation response of the trigger hair to the external mechanical stimulus. It was established that significant bending deformation occurred in the basal podium, while the trigger hair did not undergo any bending deformation. And based on the relevant theories of material mechanics, the rationality of the structure of the Venus flytrap trigger hair was verified. To further investigate this finding, we considered two additional cantilever beam structures, a notch structure and a cantilever with uniform structure, and repeated the simulations. The results indicate that the cantilever structure morphology strongly affects the location of the high strain distribution. It is probable that these regions are strain “hotspots”.

2. Materials and Methods

2.1. Experimental Material

B52 Venus flytraps, with a length when fully matured of between 2 and 3 cm, were carefully nurtured in 480 mL plastic pots, ensuring a balanced light and dark photoperiod cycle of approximately 12 h each, all while maintaining an optimal room temperature of about 22 °C. The cultivation medium used was well drained peat moss, providing the ideal conditions for their growth and development. All experiments were performed on healthy leaves.

2.2. Freeze Drying and Metal Spraying of Venus Flytrap Trigger Hair

The freeze dryer (FD-1-A50, Beijing Boyikang Experimental Instrument Co., Ltd., Beijing, China) was pre-cooled for approximately 30 min until the container temperature reached −50 °C. Thereafter, pre-frozen traps were carefully placed in the freezer dryer’s container. Following the freeze drying treatment, a layer of platinum was sprayed onto the sample surface using an Ion Sputtering Apparatus (E-1010, HITACHI, Tokyo, Japan).

2.3. Observations of the Morphology and Structure of Venus Flytrap Trigger Hair

SEM (EVO 18, ZEISS, Oberkochen, Germany) was used to examine the structural features of trigger hairs located on the inner surface of traps. And the 3D structures of trigger hairs were reconstructed using the MIMICS 21.0 (Materialise Inc., Leuven, Belgium).

2.4. Nanoindentation Experiments of Venus Flytrap Trigger Hair Lever and Basal Podium

The elastic modulus of the trigger hair lever and basal podium were measured using Piuma Nano-indenter (Optics11, Amsterdam, The Netherlands). To minimize the influence that may be induced by the hollow structure of the trigger hair, an indentation depth mode and a tested different indentation depth from 10 to 50 μm were employed. Then, the indentation data were imported into the professional data analysis software (Optics11 Date Viewer V2.5.0).

3. Results and Discussion

3.1. The Characteristics of the Venus Flytrap Trigger Hair

The B52 Venus flytrap is a typical carnivorous plant, known for its larger and more robust traps compared to other varieties. The trapping structure of the B52 Venus flytrap includes trigger hairs, midrib, leaf lobes and toothed tines, and there are three or four trigger sensory hairs distributed on the upper side of each lobe (Figure 1a). The outer surface of the trigger hair is red, as indicated in Figure 1a. Each trigger sensory hair is composed of two kinds of tissues: a flexible short basal podium and a stiff long hair lever. The length of the hair lever is 800–3000 μm, and the length of the basal podium is about 80–120 μm. The diameter of the lever increases gradually from the top to the base. And the maximum diameter of the lever is in the range of 60–200 μm. There is a notch structure located at basal podium, as shown in Figure 1d(I). Many studies have revealed that the kidney-like shaped sensory cells are distributed in a circular array at the notch area (Figure 1b) [15,16]. Finite element analysis using ABAQUS2019a was carried out on the model of the trigger hair of the Venus flytrap to investigate the deformation response of the trigger sensory hair to the external tactile signal. The elastic moduli of the lever and podium of the model were set to 18.167 Mpa and 138.167 Kpa, respectively. The density of the model was uniformly set to ρ = 1 g/cm³, and the Poisson’s ratio was set to ν = 0.3. The results clearly indicated that the podium, which is the strain concentration area of the trigger hair, experienced significant bending deformation, while the lever, which only deflected with the podium, did not undergo any bending deformation (Figure 1c). Obviously, the Venus flytrap can ultra-sensitively detect extremely tiny tactile signals utilizing the unique cantilever-like hair as a mechanosensor [9]. Under the action of external force, the stiff lever is only deflected by an angle θ, but there is no obvious bending deformation phenomenon. This design means that trigger hair amplifies forces and concentrates stresses to a flexible basal podium, and the maximum strain occurs on the contraction area where sensory cells are located. Subsequently, the unique material composition and the deflection characteristic determining the sensing performance of the tactile sensilla were further researched.

Many studies have revealed that the mechanical properties of the materials have a great influence on the deformation of the engineered structure [17,18,19,20]. Among many physical parameters, stiffness, as a measure of a material’s resistance to elastic deformation, depends on the elastic modulus. To enhance the analysis of the mechanical properties of Venus flytrap trigger hairs, nanoindentation experiments were performed. First, fresh leaves of the Venus flytrap were fixed onto glass slides using glue. Then the trigger hairs were carefully excised using a blade under an optical microscope while ensuring the preservation of their complete morphological features, including an intact basal podium and hair lever. Subsequently, the excised trigger hairs were quickly adhered to the glue, as well as ensuring that most of the volume of the trigger hairs was not submerged in the glue. Once the glue was solidified, an uncontaminated sample was obtained (Figure 2a). 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 to further carry out theoretical analysis, the structural parameters of the basal podium and the trigger hair lever are summarized in

Table 1. Structural parameters of the basal podium and hair lever.

Parameter	Symbol	Value (μm)
Length of hair lever	La	3297.32 ± 53.58
Length of basal podium	Lb	114.05 ± 35.43
Diameter of hair lever	D2	180.79 ± 13.03
Diameter of basal podium	D1	183.45 ± 5.33

.

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 θ of the cantilever beam can be expressed as:

$$\theta =\int \frac{d^{2}w}{d{x}^2}=\int \frac{M\left(x\right)}{EI}dx$$

(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. M(x) is the bending moment in different areas of the beam.

Then, the deflection w of the beam can be expressed as:

$$w=\int \theta dx$$

(2)

Combined Equations (1) and (2), the w is further given by:

$$w=\int \frac{M\left(x\right)}{EI}dx+C_{1}x+C_2$$

(3)

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:

$$w_a={\theta }_b·L_a+{\omega }_{a_0}$$

(4)

$$w_a=\frac{F{L}_b^2{L}_a}{2E_{1}I}+\frac{F{L}_a^2{L}_b}{E_{1}I}+\frac{F{L}_a^3}{3E_{2}I}$$

(5)

Here, the E₁ and E₂ are the elastic modulus of the hair’s podium and lever, respectively. $L_b$ and $L_a$ are their respective lengths.

Similarly, if the hair lever is regarded as a rigid body, the $w_b$ caused by the bending deformation of the basal podium can be given by:

$$w_b=\frac{F{L}_a{L}_b^2}{2E_{1}I}+\frac{F{L}_b^3}{3E_{1}I}$$

(6)

Based on the superposition principle of material mechanics, the maximum deflection of the whole tactile hair, $\Phi$, can be given by:

$$\mathsf{\Phi }=w_a+w_b=\frac{F{L}_b^3}{3E_{1}I}+\frac{F{L}_b^2{L}_a}{E_{1}I}+\frac{F{L}_a^2{L}_b}{E_{1}I}+\frac{F{L}_a^3}{3E_{2}I}$$

(7)

The results indicate that the hypersensitive sensing of tactile signals is achieved through the deflection characteristic of a specially constructed cantilever structure rather than the traditional bending characteristic.

3.2. Mechanical Characteristics of the Venus Flytrap Trigger Hair

Inspired by the Venus flytrap trigger hair, the mechanical characteristics of the cantilever beam is a key factor in determining the sensitivity of the trigger hair. To further discuss the relationship between the external tactile load and the maximum tensile strain, a simulated trigger hair cantilever beam model (STHCBM) was created for theoretical simulation analysis. The first step was to create two models of the STHCBM, each consisting of two sections: a podium and a lever. It is worth noting that the podium of the STHCBM has a notch structure. The schematic diagram in Figure 3 illustrates the STHCBM and how it responds to external force $F$. The STHCBM consists of two parts: a fixed podium and a free lever. The lever consists of a length $L_a$, diameter $D_2$, and elastic modulus $E_2$. The podium consists of a length $L_b$, diameter $D_1$, and elastic modulus $E_1$.

The STHCBM is a two-stage cantilever beam structure with variable stiffness, and the elastic modulus of the trigger hair lever and the basal podium are different.

The elastic coefficient K of the STHCBM is:

$$K=\frac{F}{\mathsf{\Phi }}=\frac{3E_1{I}_1{E}_2{I}_2}{L_b{E}_2{I}_2\left(L_b^2+3L_a^2+3L_b{L}_a\right)+L_a^3{E}_1{I}_1}$$

(8)

In addition, when the external force causes the bending and deforming of the STHCBM, the internal STHCBM will also produce the corresponding stress. According to solids mechanics, when any part of the lever is acted on by $F$, the stress at any section of x on it can be expressed as:

$$\sigma =\left\{\begin{array}{c}\frac{64y\left(x_f-x\right)}{\pi D_1^4}F, 0\le x\le L_b\\ \frac{64y\left(x_f-x\right)}{\pi D_2^4}F, L_b\le x\le x_f\\ 0, x_f\le x\le L_b+L_a\end{array}\right.$$

(9)

The y is the distance between the point where the stress is calculated and the neutral axis. It can be seen from Equation (9) that the maximum stress in the section of STHCBM occurs at the periphery of the section, and the stress reaches the maximum at the fixed end of the base, which decreases linearly with the increase in x.

For the STHCBM cantilever beam, the podium is the main area of deformation, which is the area of stress concentration, and the lever is the area of obvious displacement change. When the external force is applied to the free end of the STHCBM, the surface stress at the extrados and intrados of the podium section is:

$$\sigma =\frac{32\left(L_b+L_a-x\right)}{\pi D_1^3}F$$

(10)

By combining Equation (10) and substituting it into Equation (10), the relation between the maximum stress of the section at any x at the base of the STHCBM and the displacement of the free end can be obtained:

$$\sigma =\frac{3\pi E_1{E}_2{D}_1{D}_2^4\left(L_b+L_a-x\right)}{2{\pi [L}_b{E}_2{D}_2^4\left(L_b^2+3L_a^2+3L_b{L}_a\right)+L_a^3{E}_1{D}_1^4]}\mathsf{\Phi }$$

(11)

Further, a notch structure with a gradually decreasing sectional size is designed at the base of the STHCBM. The diameter of the smallest size on the notch structure is d, and the distance from the fixed end is $X_d$, and other geometric parameters remain unchanged. According to engineering mechanics, STHCBM has a further stress concentration effect on the notch structure, and the maximum stress at the notch structure is:

$${\sigma }_d=\frac{32\left(L_b+L_a-x_d\right)}{\pi d^3}F$$

(12)

According to Equation (13), the maximum stress at the fixed end of the STHCBM is:

$${\sigma }_b=\frac{32\left(L_b+L_a\right)}{\pi D_1^3}F$$

(13)

The stress amplification factor $K_{\sigma }$ of the notch structure is defined as the ratio of ${\sigma }_{d }$ and ${\sigma }_b$, so the stress amplification effect of the notch structure is:

$$K_{\sigma }=\frac{{\sigma }_{d }}{{ \sigma }_b}=\frac{\left(L_b+L_a-x_d\right)D_1^3}{\left(L_b+L_a\right)d^3}$$

(14)

As per Equation (14), the stress amplification effect of the notch structure is stronger when its minimum size $d$ is smaller and closer to the base’s bottom. Consequently, this leads to a higher stress sensitivity of the STHCBM.

In addition to the research on the sensitivity of tactile perception, stability is also a crucial consideration for STHCBM as it directly impacts its ability to resist deformation and return to its original equilibrium position under external loads. Consequently, optimizing stability is essential for ensuring optimal performance and reliability in real-world applications. When the STHCBM is not subjected to external load, its own gravity is an important factor affecting the stability of the structure, especially the flexible podium, which is easy to destabilize. According to the stability theory of a compression rod, when the trigger hair bends slightly under the action of axial force and/or lateral force (Figure 4a), and when the external force disappears, the rod can return to its original equilibrium position; this is called stable equilibrium (Figure 4b). However, when the axial force F gradually increases to a certain value$F_{cr}$, the rod will deviate from its original position, and it will not return to its original position after the external force is removed, but will maintain balance at a certain position (Figure 4c). At this time, if $F$ further increases, the rod will be further bent until it breaks. This shows that the original vertical balance of the compression rod is unstable, which is called unstable balance. When $F\ge F_{cr}$, the trigger hair will lose stability. So $F_{cr}$is called critical force, which is expressed as:

$$F_{cr}=\frac{{\pi }^{2}EI}{{\left(\mu l\right)}^2}$$

(15)

where E is the elastic modulus, I is the inertia moment of trigger hair, and l is the length of the whole hair.

If the bending stiffness $E$ and $I$ of the trigger hair are different in different planes, the lever will bend in the plane with the minimum bending stiffness. For a cantilever beam structure with variable stiffness, its critical force can be expressed as:

$$F_{cr}=\frac{{\pi }^2{E}_{min}{I}_{min}}{{\left(2l\right)}^2}$$

(16)

When the rod bears an axial load, it will transition from a balanced state to an unbalanced state, and the average stress on the section of transition critical state is called critical stress, which can be expressed as:

$${\sigma }_{cr}=\frac{F_{cr}}{A}=\frac{{\pi }^{2}E}{{\left(\mu l\right)}^2}\frac{I}{A}=\frac{{\pi }^{2}E}{{\left(\frac{\mu l}{i}\right)}^2}$$

(17)

Among,

$$i=\sqrt{\frac{I}{A}}$$

(18)

$i$ is the inertia radius of the section, and A is the section area. And:

$$\lambda =\frac{\mu l}{i}$$

(19)

Bring Equations (18) and (19) into Equation (17), then Equation (17) becomes:

$${\sigma }_{cr}=\frac{{\pi }^{2}E}{{\left(\lambda \right)}^2}$$

(20)

$\lambda$ is called the flexibility or slenderness ratio of the trigger hair, which comprehensively reflects the influence of the length, section and end constraint conditions of the rod on the critical stress. According to Equation (20), the elastic modulus of the STHCBM with variable stiffness at the podium is far less than that of the lever, so the podium is the main area where instability occurs. Based on Equation (20), reducing the flexibility of the podium material, shortening the podium length and increasing the inertia radius of the dangerous section of the podium are all effective ways to improve the stability of the STHCBM. In addition, when the STHCBM is placed vertically and the podium is fixed, the lever will exert axial pressure on the podium in this state. Therefore, when the gravity of the lever does not exceed the equilibrium critical load of the podium, it will be stable. So, reducing the mass of the lever is also an effective measure to improve the stability of the STHCBM. Based on SEM experimental observations, it has been found that the trigger hair of Venus flytraps is made up of a honeycomb tubular structure (as depicted in Figure 1d(III)). This unique structural design is an effective strategy employed by nature to minimize the weight of the lever and consequently enhance the stability of the trigger hair.

Here, to clearly display the specific meaning of symbols in formulas, a table including the major symbols mentioned earlier is listed as

Table 2. The meaning of the major symbols in formulas.

Symbols	Meanings	Symbols	Meanings
$w$	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	${\sigma }_{cr}$	Critical strain
$D_2$	Diameter of lever	$F_{cr}$	Critical strain

:

3.3. 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/cm³, and Poisson’s ratio was set as ν = 0.3.

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. Different material parameter settings ($L_1$ = 5 mm, $L_2$ = 10 mm).

Samples	E1 (MPa)	E2 (MPa)
1	1	1
2	1	2
3	1	5
4	1	10
5	1	100
6	1	500
7	2	500
8	5	500
9	10	500
10	100	500
11	500	500

.

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. In addition, when $E_2$ = 500 MPa was fixed, the deflection of the STHCBM decreased with the increase in $E_1$. The results indicate that the deflection of STHCBM remained unchanged when the ratio of $E_1/E_2$ overtakes 0.2, which certifies that a higher elastic modulus of the lever and podium reduces the deflection of the trigger hair.

However, the maximum strain at the podium of the STHCBM is not affected by the elastic modulus of the lever ($E_2$), and the maximum values occur at the bottom surface of the podium. As shown in Figure 7a, the deformation area of homogeneous STHCBM ($E_1$ = $E_2$ = 1 MPa) is scattered. On the contrary, there is no strain at the lever of the heterogeneous STHCBM ($E_1$ = 1 MPa $E_2$ = 10 MPa). The strain is mainly concentrated at the podium, and there is an obvious strain ‘boundary’ (Figure 7b). Obviously, the maximum strain at the podium is related to its elastic modulus, as shown in Figure 7c. When $E_2$ remains constant at 500 MPa, the maximum strain value decreases with the increase in the elastic modulus $E_1$.

We can draw the conclusion that when the elastic modulus of the podium is fixed, raising the ratio of the elastic modulus of the STHCBM lever to the podium can effectively reduce the deflection of the trigger hair, and the maximum strain of the podium will not be affected. Under the same action of a force, a heterogeneous STHCBM with a high elastic modulus ratio only needs a smaller displacement signal to achieve the same strain concentration effect as a traditional homogeneous STHCBM, and effectively reduces the strain distribution area.

Subsequently, the influence of geometric parameters on the mechanical properties of the STHCBM was also worth analyzing. Under the same material parameters ($E_1$ = 1 MPa, $E_2$ = 10 MPa), the relationship between the maximum deflection and the length of the podium ($L_b$) and lever ($L_a$) is further discussed below (

Table 4. Different geometric parameter settings of STHCBM.

Samples	La (mm)	Lb (mm)
1	10	0
2	10	5
3	10	10
4	10	15
5	10	20
6	0	10
7	5	10
8	15	10
9	20	10

).

The simulation results are shown in Figure 8a,b. The results indicate that longer $L_b$ and $L_a$ directly improve the maximum deflection of the STHCBM, respectively. Obviously, when the total length is fixed, the deflection of the larger proportion of the lever length is greater. Figure 8c shows that, under the same concentrated force, the longer the total length, the greater the maximum strain would be at the podium. On the other hand, the maximum stress at the podium increases with the increase in the force. Hence, the change trend of the maximum deflection is consistent with the maximum stress.

Cantilever-type sensors can effectively transmit and amplify external input signals, leading to a significant improvement in their performance [24,25,26,27]. Therefore, the principle of optimizing cantilever beam structure is to enhance their response sensitivity to external mechanical signals by reducing strain regions and increasing strain extremes, while ensuring stability. A notch structure inspired by the structure of Venus flytrap trigger hair is introduced here. The minimum diameter of the notch structure is d = 0.6 mm, and the distance from the fixed end of the podium is $X_d$ = 2 mm, and other parameters remain unchanged. As shown in Figure 9a,b, similar to a STHCBM without notch structure, there is almost no deformation, which is caused by the strain, occurring on the hair lever. The strain of a STHCBM mainly concentrates on the podium. However, the difference is that the strain of the STHCBM with notch structure is more concentrated and four times higher than that of the STHCBM without notch structure. The influence of the geometric parameters of the notch structure in the podium on the strain of the STHCBM is further analyzed. Firstly, keep the minimum diameter of the notch structure d = 0.6 mm unchanged and changed its distribution position on the podium. The results are shown in Figure 9c, the closer the notch structure to the fixed end of the podium, the greater the strain extreme value will be. In addition, when the distribution position $X_d$ = 2 mm of the notch structure was constant, and its minimum diameter d changed. As shown in Figure 9d, the smaller the minimum diameter of the notch structure, the larger the strain concentration effect on it and the strain extreme value will be.

The above research on the maximum strain of the cantilever beam effectively demonstrates that the diverse characteristics of the trigger hair are beneficial for improving the sensitivity of trigger hair. Therefore, the combination of the characteristics, including a more flexible podium, longer hair, a lighter lever, and a larger constriction structure close to the bottom, is a unique strategy for designing a cantilever sensor that performs well with a good balance between high sensitivity and persistent stability. As a result, based on previous research on the stability of STHCBM, incorporating a notch structure can effectively enhance its sensitivity. However, it is important to note that the introduction of a notch structure may also compromise the overall stability of the STHCBM. Therefore, the optimization of balancing both sensitivity and stability is shown in Figure 10. First of all, for the traditional homogeneous cantilever beam structure, under the action of external forces, there will be strains distributed on the lever, but the strain regions were scattered, and the strain extremes were low (Figure 10I). In order to narrow the strain concentration area and reduce the dispersion of strain energy, a measurement of increasing the elastic modulus of the hair lever to enhance its stiffness was taken. In this case, the strain was concentrated at the podium of the cantilever beam (Figure 10II). On the basis of variable stiffness, a gradual notch structure was installed at the podium of the cantilever beam, and as Figure 10III shows, the notch structure made the strain further concentrated and effectively increased the extreme strain value. Furthermore, in order to improve the overall stability of the cantilever beam, a honeycomb tubular structure lever was necessary. In this case, the axial load caused by the dead weight of the lever at the podium will be smaller, and compared to the solid lever, the honeycomb tubular structure can be designed longer to further enhance the sensitivity of the cantilever beam (Figure 10IV).

4. Conclusions

In summary, building upon prior research, this article utilizes scanning electron microscopy to investigate the contact of Venus flytrap trigger hairs. The study also applies material mechanics and finite element analysis software for theoretical derivation. The trigger hairs of the Venus flytrap were characterized by a cylindrical cantilever beam structure. However, unlike typical homogeneous cantilever beams, the trigger hairs of Venus flytraps have a unique notched and variable stiffness structure. This work may provide inspiration for biological research and the design of industrial sensors.

(1)

Based on the observed structure of Venus flytrap hair and previous research, three-dimensional modeling was conducted. Then, the relevant material mechanics theories and finite element analysis software were used to analyze homogeneous cantilever beams and variable stiffness cantilever beams. The results reveal that when exposed to identical external force stimulation, a homogeneous cantilever beam disperses the strain, whereas a variable stiffness cantilever beam concentrates the strain at the podium, creating a clear boundary of strain.

(2)

In addition, a comparative and analytical study on the performance of a cantilever beam with variable stiffness, both with and without notch structure subjected to external stimuli, was conducted. The findings suggest that the utilization of a notch structure in a variable stiffness cantilever beam can effectively concentrate strain and significantly enhance its extreme value.

(3)

During the discussion, how the size parameters of STHCBM can impact their strain and stress was explored. Specifically, longer beams displayed higher values of strain and stress when subjected to the same external force. This result suggests that longer beams may be more effective at amplifying external stimulus signals.

(4)

Finally, the stability of the STHCBM and utilized finite element software analysis were investigated to demonstrate that the hollow design of various cantilever beams can significantly enhance overall stability. The structural composition and sensory mechanisms of Venus flytrap hairs offer a novel source of inspiration for the development of future cantilever sensors, with potential for enhanced accuracy and functionality.