## 2 Debonding Detection with Electromechanical Impedance Technique  
Before introducing the biomimicry idea, we first need to identify the limitation of conducting the EMI technique using the conventional approach of attaching the PZT (lead-zirconate-titanate) transducer. The setup for the EMI technique used for this section can be seen in Figure 1. By connecting the AD5933 evaluation board (manufactured from Analog Devices co., Wilmington, MA, USA) onto a computer and the PZT transducer (model 5A4E, purchased from Piezo.com), one can acquire impedance signatures using the provided software to conduct the EMI technique. The AD5933 evaluation board can measure impedance up to 100 kHz with more than 500 data points where the USB data cable also provides enough power to run the device. According to the one-dimensional equation proposed by [PERSON] et al. (1994) in Equation (1), the electrical admittance \(Y(\omega)\) is a combined function of \(Z_{s}(\omega)\) and \(Z_{a}(\omega)\), which are the mechanical impedance of the host structure and the PZT transducer, respectively. This means that any change in structural properties (such as damage) can be detected by measuring the electrical impedance of the PZT transducer attached to the host structure. Other variables in the equation, which are \(I\), \(V\), \(\omega\), \(a\), \(\varepsilon_{33}^{T}\), \(\delta\), \(d_{3x}\), \(\overline{Y}_{xx}^{E}\) represent the PZT output current, PZT input voltage, input frequency, geometric constant, dielectric constant, loss tangent, piezoelectric constant and [PERSON]'s modulus, respectively. \[Y(\omega)=i\omega a\bigg{(}e_{33}^{T}(1-i\delta)-\frac{Z_{s}(\omega)}{Z_{s}( \omega)+Z_{a}(\omega)}d_{3x}^{2}\overline{Y}_{xx}^{E}\bigg{)} \tag{1}\]  
Two 0.6 mm thickness glass fiber reinforced epoxy composite plates shown in Figure 1 is attached to each other using an epoxy adhesive (quick-set Epoxy, Loctite, Dusseldorf, German) where the test specimen was divided into 8 areas labelled A1 to A8. Within each area, a small part was debonded (3 cm \(\times\) 3 cm) where the impedance signatures were measured after debonding from each of the 8 areas. This resulted in a total number of 9 signatures which can be seen in Figure 2.  
Figure 1: Experimental setup for detecting debonding damage on composites. Observing Figure 2, we notice that there are only small peaks along the impedance signatures. With a closer look, the variations can be seen at around 32 kHz, 41 kHz and 47 kHz with the amplitude of the peaks changing. Next, to quantify the severity of damage, RMSD (root mean square deviation) values were calculated for the debonding damage for each area where the two impedance signatures before and after the debonding damage were used to calculate the RMSD values. The RMSD values have been used to analyze the EMI technique in general as it has been found to be effective in identifying damage by various researchers. The equation on RMSD is shown below where \(Z_{i}^{o}\) and \(Z_{i}\) represents the signatures before and after damage, respectively. The variable \(N\) in the equation represents the number of the impedance signature:  
\[\text{RMSD}=\sqrt{\sum_{N}\bigl{[}Re\bigl{(}Z_{i}\bigr{)}-Re\bigl{(}Z_{i}^{o} \bigr{)}\bigr{]}^{2}/\sum_{N}\bigl{[}Re\bigl{(}Z_{i}^{o}\bigr{)}\bigr{]}^{2}}. \tag{2}\]  
The calculated RMSD values are labeled in the right side of Figure 2 where the values can be seen for each area (A1 to A8). Looking at the figures, the highest RMSD value was observed for A1 with 0.5 with the lowest being 0.31 for A4 and A6. Although all the areas have similar distances to the PZT transducer attached in the middle of the composite structure, there are differences in the RMSD values. In addition, one can say the 0.5 is about 1.6-7 times larger than the 0.31. One of the reasons for such a difference is due to the fact that the impedance signature keeps changing as debonding damage is given to the structure.