## 3 Results and Discussion
Therefore, the surface membrane must protect the pre-existing mechanosensory slit through controlling the slit width within a safe threshold. While the above studies only reveal the protective mechanism of the surface membrane, there is still no reasonable interpretation of how the membrane avoids negative effects on sensing accuracy when a weak vibration signal acts on the BCSS. Hence, we further determined the functional relationship between \(E_{c}\) and slit width \(w\) based on Equations (10)-(12):  
\[E_{c}=\left\{ \begin{array}{ll}\frac{E_{c}}{1+\big{(}\frac{E_{c}}{E_{m}}-1 \big{)}\big{[}1+\gamma\big{(}\frac{w}{2t_{m}}\big{)}\big{(}\frac{E_{m}}{E_{s} }-1\big{)}\big{]}^{-1}},&w<2t_{m}\\ \frac{E_{s}}{1+\big{(}\frac{E_{c}}{E_{m}}-1\big{)}\big{[}1+\gamma\big{(}\frac {w}{2t_{0}}\big{)}\big{(}\frac{E_{m}}{E_{s}}-1\big{)}\big{]}^{-1}},&w>\text{w} _{0}\end{array} \right. \tag{13}\]  
The \(E_{c}\) as a function of \(w\) based on Equation (13) is plotted in Figure 2e. The result indicates that, consistent with the finding in Figure 1f, there is bending deformation occurring in the membrane tissue during the signal detection process (i.e., \(5~{}\upmu\text{m}<\omega<8~{}\upmu\text{m}\)). The bending stiffness, which can effectively represent the ability of material to resist bending deformation, is given by  
\[EI=Ebt^{3} \tag{14}\]  
where \(EI,E,b,t\) are the bending stiffness, elastic modulus, width and thickness of the component, respectively. Figure 2a shows that the width (\(b\)) of the exoskeleton and surface membrane are equal in the structural model. Therefore, the ratio (\(H\)) of exoskeleton bending stiffness (\(E_{s}l_{s}\)) and membrane bending stiffness (\(E_{m}l_{m}\)) can be presented as \(H=E_{s}t_{e}^{3}/E_{m}t_{m}^{3}\). The calculation result indicates that \(H\approx 8\times 10^{4}\), which futher clearly shows that the membrane tissue is more prone to bending deformation than the exoskeleton if the width of the slit is in the range of \(5~{}\upmu\text{m}<\omega<8~{}\upmu\text{m}\). Furthermore, Figure 2f shows that the three-dimensional morphology of the slit wake is typically concave which is easily subjected to a bending moment. Under the action of the bending moment, the surface membrane, with extremely small bending stiffness, undergoes bending deformation in the process of signal detection, which does not influence the sensing performance of the slit unit. In order to further verify the functional mechanism of the surface membrane, we performed finite element simulations based on ANSYS software. The 3D finite element model of a substrate and film is shown in Figure 4a. The crack was modeled at the edge of the substrate. The wake of crack is covered by a layer of polyester film. Similar to the biological material around the slit wake, the elastic modulus ratio of the film and the substrate in this model is about 0.1. In the finite element analysis, constraints are imposed on the left end of the substrate, and a tensile or compressive load is applied on the other end for analyzing the change of stress intensity at the film surface and the tip of the crack. The stress concentration coefficient [31], as a parameter reflecting the degree of local stress increase, was used to characterize the influence of surface membrane on the stress intensity at the slit tip. Figure 4b shows that the surface membrane is compressed, bended and stretched, respectively, with the change of slit width, which is in good agreement with the results of the present experiments and theoretical analysis. Meanwhile, the stress concentration coefficient decreases significantly at the stages of tension and compression, but remains constant in the bending stage. In the absence of the membrane, the stress concentration coefficient keeps constant with the change of slit width (Figure 4b), which is consistent with the bending deformation stage of the membrane. The above results further indicate that the stress intensity at the crack tip is only restrained by the surface membrane under compression and tension.