## 2 Experimental Material and Method
### Experimental Apparatus and Principle
In accordance with the stress wave theory, the displacement function \(u(t)\) of a point on the sine wave can be expressed as:  
\[u(t)=C\int_{0}^{t}\varepsilon(t)\mathrm{d}t \tag{1}\]  
where \(C\) represents the stress wave velocity in the media (bars), whilst \(t\) and \(\varepsilon(t)\) denote the time and strain function with respect to time, respectively. Assuming the strain functions of the three types of the stress waves are \(\varepsilon_{\mathrm{i}}(t)\), \(\varepsilon_{\mathrm{r}}(t)\) and \(\varepsilon_{\mathrm{t}}(t)\), respectively, the horizontal displacement functions (\(u_{1}(t)\) and \(u_{2}(t)\)) on the I and II interfaces in Figure 4 could be written as:  
\[\left\{ \begin{array}{ll}u_{1}(t)=C\int_{0}^{t}\left(\varepsilon_{\mathrm{i}} (t)-\varepsilon_{\mathrm{r}}(t)\right)\mathrm{d}t\\ u_{2}(t)=C\int_{0}^{t}\varepsilon_{\mathrm{t}}(t)\mathrm{d}t\end{array} \right. \tag{2}\]  
If the sample length is denoted as \(L_{\mathrm{s}}\), the dynamic strain function \(\varepsilon_{\mathrm{s}}(t)\) can be expressed as:  
\[\varepsilon_{\mathrm{s}}(t)=\frac{u_{1}-u_{2}}{L_{\mathrm{s}}}=\frac{C}{L_{ \mathrm{s}}}\int_{0}^{t}\left(\varepsilon_{\mathrm{i}}(t)-\varepsilon_{ \mathrm{r}}(t)-\varepsilon_{\mathrm{t}}(t)\right)\mathrm{d}t \tag{3}\]  
Figure 4: Experimental principle and equipment: (**a**) schematic of SHPB system, and (**b**) SHPB components. In accordance with the uniformity hypothesis, Equation (3) can be rewritten by substituting \(\epsilon_{\rm t}(t)=\epsilon_{\rm i}(t)+\epsilon_{\rm r}(t)\), namely,  
\[\epsilon_{\rm s}(t)=-\frac{2C}{L_{\rm s}}\int_{0}^{t}\epsilon_{\rm r}(t)\mathrm{ d}t \tag{4}\]  
By differentiating Equation (4) with regard to \(t\), then the strain rate of the specimen could be deduced as:  
\[\dot{\epsilon}_{\rm s}(t)=\frac{2C}{L_{\rm s}}\epsilon_{\rm r}(t) \tag{5}\]  
Obviously, the two forces imposing on the two end surfaces of the specimen could be obtained by:  
\[F_{1}=EA_{\rm i}(\epsilon_{\rm i}(t)+\epsilon_{\rm r}(t)),\ F_{2}=E_{\rm t}A_{ \rm i}\epsilon_{\rm t}(t) \tag{6}\]  
where \(F_{1}\) and \(F_{2}\) mean the forces acting on the top and bottom ends of the specimen, respectively. \(E_{\rm i}\) and \(A_{\rm i}\) represent the Young's modulus and cross sectional area of the incident bar, while \(E_{\rm t}\) and \(A_{\rm t}\) mean those of the transmitted bar. In this research, \(E=E_{\rm i}=E_{\rm t}\) and \(A=A_{\rm i}=A_{\rm t}\). Based on Equation (6), it is quite easy to solve the dynamic stress in the specimen by:  
\[\sigma_{\rm s}(t)=\frac{F_{1}+F_{2}}{2A_{\rm s}} \tag{7}\]  
where \(\sigma_{\rm s}(t)\) and \(A_{\rm s}\) denote the average internal stress and cross sectional area of the specimen, respectively. In this study, we define the tensile stress as positive and compressive stress as negative. Combining Equations (6) and (7), leads to:  
\[\sigma_{\rm s}(t)=E\bigg{(}\frac{A}{2A_{\rm s}}\bigg{)}[\sigma_{\rm i}(t)- \sigma_{\rm r}(t)+\sigma_{\rm t}(t)]=E\bigg{(}\frac{A}{A_{\rm s}}\bigg{)} \epsilon_{\rm t}(t) \tag{8}\]  
in which \(\sigma_{\rm i}(t)\), \(\sigma_{\rm r}(t)\) and \(\sigma_{\rm t}(t)\) denote the absolute values of the incident, reflected and transmitted stresses with respect to the loading time \(t\). From Equations (3) and (4), the expressions of and \(\epsilon_{\rm s}(t)\) could be further obtained by:  
\[\dot{\epsilon}_{\rm s}(t)=\frac{C}{EL_{\rm s}}(\sigma_{\rm r}(t)+\sigma_{\rm t }(t)-\sigma_{\rm i}(t)) \tag{9}\]  
\[\epsilon_{s}(t)=\int_{0}^{t}\dot{\epsilon}(t)dt \tag{10}\]  
To sum up, according to the obtained strain signals, the real-time dynamic mechanical property parameters of the sample can be solved by Equations (8)-(10). Evidently, the dynamical strength of the sample is positively related to the strain of the transmitted wave.