# Dynamic Response of Electro-Mechanical Properties of Cement-Based Piezoelectric Composites
## 2 Materials and Methods
### Performance Test  
The Mechanical Testing System (MTS) is used to perform quasi-static compression tests on type 1-3 and type 2-2 cement-based piezoelectric composite samples. The alumina ceramic column is used to insulate the sample surface against the testing machine and output a high-impedance charge signal, which is converted into a low-output-impedance voltage signal via a charge amplifier; subsequently, the data signal is collected by the data collector and transmitted to the computer for processing, saving, and analyzing data. According to the cyclic loading characteristics, the initial stress value and loading frequency are controlled and the stress amplitude is increased sequentially; this causes the corresponding electric displacement to also increase. The initial stress value is 0 and the frequency is 1 Hz. By determining the peak value of the electric displacement and fitting it into a straight line, the quasi-static sensitivity of the type 1-3 and type 2-2 cement-based piezoelectric composite samples can be obtained. The ratio of the output electric displacement \(D(t)\) to the stress \(\sigma(t)\) represents the static sensitivity of the sample.  
An SHPB device is used to perform impact compression tests on type 1-3 and type 2-2 cement-based piezoelectric composites. The SHPB device are shown in Figure 3. The lengths of the impact bar, incident bar, transmission bar, and absorption bar are 400, 2000, 2000, and 600 mm, respectively; the bar diameter is 37 mm, and the material used is high-strength spring steel. According to the one-dimensional stress wave and homogenization assumption of the SHPB technology, the stress \(\sigma_{s}(t)\), strain \(\varepsilon_{s}(t)\), strain rate \(\hat{\varepsilon}_{s}(t)\) and average strain rate \(\hat{\varepsilon}\) of the sample can be calculated via Formulas (1)-(4) [28], respectively.  
Figure 1: Samples of cement-based piezoelectric composites.  
Figure 2: Packaged structure of the sample. (**a**) Schematic of the packaged structure; (**b**) Actual image of the packaged structure.  
Ordinary strain gauges are attached to both the incident and transmission bars to record the stress waveform in the bar during the test. To increase the rising edge time of the loading waveform and balance the internal stress of the sample, a brass wave shaper is attached to the front face of the incident bar.  
\[\sigma_{S}(t)=\frac{EA}{A_{0}}[\varepsilon_{I}(t)+\varepsilon_{R}(t)] \tag{1}\]  
\[\varepsilon_{S}(t)=\frac{2c_{0}}{L_{0}}\int_{0}^{t}[\varepsilon_{I}(t)- \varepsilon_{T}(t)]dt \tag{2}\]  
\[\dot{\varepsilon}_{S}(t)=\frac{2c_{0}}{L_{0}}[\varepsilon_{I}(t)-\varepsilon_ {T}(t)] \tag{3}\]  
\[\dot{\tilde{\varepsilon}}=\frac{\int_{0}^{\epsilon}\dot{\varepsilon}_{s}( \varepsilon)dt}{\varepsilon_{s}} \tag{4}\]  
Here, \(E\) is the elastic modulus of the steel bar, \(A\) is the cross-sectional area of the steel bar, \(C_{0}\) is the propagation speed of the stress wave signal in the steel bar, \(A_{0}\) is the cross-sectional area of the sample, \(L_{0}\) is the length of the sample, \(\varepsilon_{I}(t)\) is the incident wave signal, \(\varepsilon_{R}(t)\) is the reflected wave signal on the incident bar, and \(\varepsilon_{T}(t)\) is the transmitted wave signal on the transmission bar.