## 3 Results and Discussions
### Analysis and Discussions of the Element Parameters  
To provide deeper insight into the influence of the strain on the element parameters of the equivalent circuit model, we plotted the element parameter values as functions of the strain. The resistances \(R_{1}\), \(R_{2}\), \(R_{3}\) and \(R_{4}\) increased with the strain as illustrated in Figure 6a. This can be mainly attributed to two factors. First, the formation and extension of microcracks leads to the breakdown of the conductive pathways. Second, the elongation of the AgMP/PDMS composite leads to an increase of the resistivity of the composite. This is because the distance between AgMP fillers become bigger during the stretching, leading to damage of the conductive networks [24]. These two mechanisms can be revealed by the DC resistance of the strip conductor. Here, a digital multimeter (UT71B, Uni-Trend Technology Inc., Beijing, China) was used to monitor the real-time DC resistance of the strip conductor. The relative resistance change (\(\Delta R/R_{0}\)) under strain was shown in Figure 6b. It rose slowly with a relatively low strain (\(\Delta\epsilon\leq 5\%\)), and then increased rapidly with higher strains (\(\Delta\epsilon\geq 5\%\)). This was consistent with the RF equivalent resistance with an increasing strain (Figure 6a). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\Delta\epsilon\) & \(R_{1}\) & \(R_{2}\) & \(R_{3}\) & \(R_{4}\) & \(L_{1}\) & \(L_{2}\) & \(C_{1}\) \\ \hline
0\% & 0.77 \(\Omega\) & 1.2 \(\Omega\) & 1.2 \(\Omega\) & 2.5 \(\Omega\) & 251 pH & 251 pH & 150 pF \\ \hline
3\% & 0.89 \(\Omega\) & 4 \(\Omega\) & 4 \(\Omega\) & 6 \(\Omega\) & 445 pH & 439 pH & 101 pF \\ \hline
5\% & 1.2 \(\Omega\) & 25 \(\Omega\) & 25 \(\Omega\) & 16 \(\Omega\) & 605 pH & 605 pH & 35 pF \\ \hline
8\% & 2.7 \(\Omega\) & 33 \(\Omega\) & 33 \(\Omega\) & 28 \(\Omega\) & 700 pH & 700 pH & 21 pF \\ \hline
10\% & 5 \(\Omega\) & 50 \(\Omega\) & 50 \(\Omega\) & 40 \(\Omega\) & 929 pH & 929 pH & 11 pF \\ \hline
12\% & 7.8 \(\Omega\) & 78 \(\Omega\) & 78 \(\Omega\) & 55 \(\Omega\) & 1.2 nH & 1.2 nH & 3 pF \\ \hline \(\Delta\epsilon\) & \(\Delta R_{1}\) & \(\Delta R_{2}\) & \(\Delta R_{3}\) & \(\Delta R_{4}\) & \(\Delta L_{1}\) & \(\Delta L_{2}\) & \(\Delta C_{1}\) \\ \hline
0\% & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
3\% & 0.12 \(\Omega\) & 2.8 \(\Omega\) & 2.8 \(\Omega\) & 3.5 \(\Omega\) & 194 pH & 188 pH & \(-\)49 pF \\ \hline
5\% & 0.43 \(\Omega\) & 23.8 \(\Omega\) & 23.8 \(\Omega\) & 13.5 \(\Omega\) & 354 pH & 354 pH & \(-\)115 pF \\ \hline
8\% & 1.93 \(\Omega\) & 31.8 \(\Omega\) & 31.8 \(\Omega\) & 25.5 \(\Omega\) & 449 pH & 449 pH & \(-\)129 pF \\ \hline
10\% & 4.23 \(\Omega\) & 48.8 \(\Omega\) & 48.8 \(\Omega\) & 37.5 \(\Omega\) & 678 pH & 678 pH & \(-\)139 pF \\ \hline
12\% & 7.03 \(\Omega\) & 76.8 \(\Omega\) & 76.8 \(\Omega\) & 52.5 \(\Omega\) & 949 pH & 949 pH & \(-\)147 pF \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The element parameters for fitting. Figure 5: The calculated S-parameters under various strains: (**a**) S11 spectra; (**b**) S21 spectra. An additional experiment was conducted by SEM observation of the microcracks under strain as shown in Figure 7. Initially, the strip conductor layer was continuous with the silver micro-particles uniformly distributed in the PDMS and no crack was found as shown in Figure 7a. When the conductor was stretched, the microcracks generated on the surface of the AgMP/PDMS film, whereas the AgMP/PDMS film was still connected around the interface between the AgMP/PDMS film and PDMS substrate as shown in Figure 7b. Further increasing the strain from 5% to 10% broadened and deepened the crack as Figure 7c shows. The width distributions of microcracks are shown in Figure 7d,e corresponding to 5% and 10% strain, respectively. The average width of the microcracks was about 5 \(\upmu\)m under 5% strain, and approximately 9 \(\upmu\)m under 10% strain. We could observe that the size of the microcrack increased with the increase of strain.