## 3 Results and Discussion
Figure 2: (**a**) Structural model of tissue around a slit wake; (**b**) simplified structural model based on (**a**) for analyzing the process of tension and compression; (**c**) the composite elastic modulus as a function of membrane strain under different values of \(Em\); (**d**) the relationship between the strain of composite tissue and applied stress under different values of \(Em\); (**e**) the deformation type of surface membrane in different range of slit width; (**f**) three-dimensional surface morphology of tissue around a slit wake. Based on the microstructural characteristics and mechanical performance of tissue around the slit wake, we further analyzed the balancing strategy of sensing accuracy and structural safety. Fracture mechanics studies have proven that the pre-existing crack will further propagate from the near-tip stress field with the excessive opening and closure of crack. Longitudinal cross-section image indicates that the tissue around slit wake can be regarded as a multi-phase laminated tissue (Figure 1e). The composite elastic modulus can effectively represent the ability of multi-phase laminated tissue to resist tensile and compressive deformation. Hence, we theoretically analyzed the composite elastic modulus (\(E_{c}\)) of tissue around a slit wake, which can easily predict the ability of the surface membrane to control the opening displacement (i.e., the width) of the slit and then further avoid new crack nucleation from the slit tip. Firstly, the multi-phase laminated structural model approximating the longitudinal section morphology is given in Figure 2a, which clearly indicates that the membrane is sandwiched between the exoskeleton. In tensile and compressive deformation of surface membranes, this structural model can be further simplified to equal the thickness model in Figure 2b, because the vertical height of the effective stress surface is equal to the thickness of the membrane. The composite elastic modulus (\(E_{c}\)) for this typical tessellated structural model in Figure 2b is calculated through an isostress description of composite behavior and given by [27]:  
\[E_{c}=\left[\frac{f_{m}}{E_{m}}+\frac{(1-f_{m})}{E_{s}}\right]^{-1}=\frac{E_{ s}}{1+\left(\frac{E_{c}}{E_{m}}-1\right)f_{m}} \tag{1}\]  
Figure 3: (**a**) Elastic modulus map of tissue around a slit wake under fresh conditions; (**b**) elastic modulus map of tissue in dehydrated state; (**c**) nano-indentation load displacement curves of membrane tissue and exoskeleton, respectively; (**d**) the elastic modulus of exoskeleton and membrane tissue calculated based on the curves in (**c**). where \(f_{m}\) is the volume fraction of membrane tissue in the tessellated structural model (Figure 2b). The \(f_{m}\) would be changed when there is stress acting on the sensilla. Hence, the \(f_{m}\) can be further given by:  
\[f_{m}=\frac{l_{m}}{(l_{m}+l_{d})} \tag{2}\]  
here, \(l_{m}\) and \(l_{d}\) are represent the width of membrane tissue and exoskeleton, respectively. The strain, \(\varepsilon_{m}\), of the membrane tissue located at the slit wake can be given by:  
\[\varepsilon_{m}=\int_{l_{m0}}^{l_{m}}\frac{dl}{l}=\ln\left(\frac{l_{m}}{l_{m0 }}\right) \tag{3}\]  
here, \(l_{m0}\) is the initial width of the membrane tissue. With the mechanical signal acting on the BCSS, the membrane tissue would experience three types of stress (i.e., tensile stress, bending stress and compressive stress), successively. At initial stage of tension, \(l_{m0}\) can be represented by the original width, \(w_{0}\), of a crack-shaped slit. At the initial stage of compression, \(l_{m0}\) is two times the thickness, \(t_{m}\), of the membrane tissue, because of the folding deformation at the bending stage (Figure 2b). In summary, the initial width, \(l_{m0}\), of membrane tissue can be given:  
\[l_{m0}=\left\{ \begin{array}{cc}w_{0},&\text{tension}\\ 2t_{m},&\text{compression}\end{array} \right.