# Bio-Inspired Mechano-Sensor Based on the Deformation of Slit Wake
## 3 Results and Discussion
The Au layer is located on the upper surface of the PET substrate. Hence, in convex bending, the nanoscale crack width increases with the bending deformation of the FUCMSS, which further leads to an increase in resistance. Conversely, in concave bending, the edges of the cracks are close to each other, resulting in a decrease in resistance. Figure 4b,\(\varepsilon\) show the relative resistance (\(\Delta R/R_{0}\)) as a function of strain (\(\varepsilon\)) about the FUCMSS under the conditions of the above two types of bending deformation. The results indicate that in concave-bending mode or convex-bending mode, there is a positive correlation between the value of \(\Delta R/R_{0}\) and the absolute value of \(\varepsilon\). However, when the FUCMSS had the same absolute value of \(\varepsilon\), the value of \(\Delta R/R_{0}\) in convex-bending mode was two orders of magnitude higher than the that in the concave-bending mode. Meanwhile, the Au film without the nanoscale crack structure was not sensitive to the bending deformation of the PET substrate. Obviously, the above analysis shows that the FUCMSS working in the convex-bending mode is more sensitive to the bending deformation. Hence, the FUCMSS working in the convex-bending mode has a greater advantage in low-mechanical-signal detection. Additionally, Figure 4c shows that the rate of the change in \(\Delta R/R_{0}\) increases significantly with the increase in bending deformation, indicating that with a certain initial bending, the sensitivity of the FUCMSS can be further improved. Figure 3: Characterization of the performance of slit-based mechano-sensor. (**a**) The resistance response of various crack-based strain sensor fabricated using different radii of slender rod. (**b**) Reversible loading-unloading behavior for various final strains. (**c**) The current-voltage (I–V) curves of crack-based strain sensor. (**d**) The response and recovery time of the crack-based strain sensor. (**e**) Relative resistance change–time curves of strain sensor for 12,000 loading/unloading cycles. (**f**) The loading–unloading curves at different stages. The deformability of the slit wake in response to low mechanical signals has a great influence on the performance of the slit-based mechano-sensor. Here, the factors affecting the deformability are systematically analyzed. According to the theory of fracture mechanics, the deformation of slit can be represented by [33]:  
\[w\approx\frac{(1+v)(3-v)}{2E}\gamma\sigma\sqrt{a^{2}-x^{2}} \tag{1}\]  
Here, \(w\) is the width of the slit, \(v\) is Poisson's ratio, \(E\) is the elastic modulus of homogeneous material, \(Y\) is the shape factor, \(\sigma\) is the applied stress, the direction of which is perpendicular to the length of the slit, \(a\) is the length of slit, \(x\) is distance from any point of the slit to the slit wake. At the slit wake, the value of \(x\) is 0. The deformation of the slit wake, \(w_{s}\), can be given by:  
\[w_{s}\approx\frac{(1+v)(3-v)}{2E}\gamma\sigma a \tag{2}\]  
Equation (2) indicates that with the decrease in elastic modulus, \(E\), the deformability of the slit wake can be effectively improved. Many studies have revealed that the \"hollowed out\" design can significantly reduce the overall stiffness of the structure, \(E_{t}\), which can be represented by:  
\[E_{t}=E(1-V_{p}{}^{2}) \tag{3}\]  
Figure 4: Two different bending-deformation mode of FUCMSS under compressive stress. (**a**) Two different types of bending deformation of the PET substrate under compressive stress and the corresponding change in resistance. (**b**) The loading–unloading curve of the FUCMSS under concave-bending deformation. (**c**) The loading–unloading curve of the FUCMSS under convex-bending deformation. Here, \(V_{p}\) is the effective removal area of the solid substrate.