## 3 Results and Discussions  
### The Equivalent Circuit Model of the Microstrip with Microcracks  
To illustrate the microcracks, Figure 3a exhibits SEM images of the fracture surfaces of the strip conductor of the microstrip. After a prestretch process, the microcracks are approximately perpendicularly oriented with respect to the strain. The microcracks illustrated moderate wavy shapes at a higher magnification as shown in Figure 3b. The microcrack was about 4 \(\upmu\)m in width with random-distributed finer microcracks of less than 0.6 \(\upmu\)m in width. We noted that the microcrack was discontinued where the AgMP/PDMS was partially bridge-connected across the microcracks, leading to some conductive paths. Similarly, the AgMP/PDMS thin film was also connected at the bottom of the microcrack. This may be attributed to the nonuniform strain distribution in the composite film. Upon stress, the strain first locates in the interfaces between the silver particles and PDMS, and then cracks nonuniformly originate and propagate in the AgMP/PDMS layer, possibly due to the tractive effort of the localized stress on the interface [22].  
Figure 3: (**a**) Scanning electron microscope (SEM) images of the microstrip with microcracks. 1 and 2 are SEM images of the complete surface and the bottom of the microcrack, respectively. (**b**) The equivalent circuit of a section of the conductor. (**c**) The equivalent circuit model of the microstrip with microcracks.  
To reveal the influence of the microcrack on RF characteristics, we proposed an RF local equivalent circuit model in accordance with the micromorphology of an identical microcrack on the AgMP/PDMS composite strip conductor, as the red lines demonstrate in Figure 3b. The microcrack with a valley-liked shape involved an insulated air gap with two conductive AgMP/PDMS scarps on both sides. This configuration can be equivalent to a microcapacitor and is marked as c\({}_{1}\). The resistors r\({}_{3}\) and r\({}_{4}\) represent the resistance where the microcrack was bridge-connected across the valley or at the bottom of the film, respectively. Considering the nonzero resistivity of the AgMP/PDMS composite film, two resistors r\({}_{1}\) and r\({}_{2}\) were also induced to the equivalent circuit to reflect the RF losses.  
From a device perspective, we proposed a \(\pi\) equivalent circuit for the whole microstrip with microcracks, which can be seen as adding the series of the local equivalent circuits to the standard RF equivalent circuit for a microstrip transmission line as stretched in Figure 3c. The equivalent-circuit elements were deduced from the local elements, which are marked in Figure 3b. The presence of resistances \(R_{1}\), \(R_{2}\), \(R_{3}\) and \(R_{4}\) were attributed to the finite conductivity of the conductor, which leads to the conductor losses and the reflection of the RF signal [23]. The resistance \(R_{4}\), related to the resistance \(r_{3}\) and \(r_{4}\) in Figure 3b, represented the equivalent resistance across the microcrack. The series inductances \(L_{1}\) and \(L_{2}\) represented the self-inductance of the conductor. The capacitance \(C_{1}\) was derived from the microcrack, and \(C_{2}\), and \(C_{3}\) were the equivalent capacitances between the conductor and ground plane for a standard microstrip transmission line.