## 2 Constitutive Relation of Modified Polydimethylsiloxane Material  
### Direct Tensile Test  
(1) Specim preparation  
Our research team [27] compared the modified polydimethylsiloxane with the sodium silicate commonly used in construction, and found that the modified material had better impermeability. The traditional uniaxial tensile test is conducted to investigate the mechanical properties of modified polydimethylsiloxane material. The specimen preparation and testing are based on a Chinese technical specification, 'Hydraulic Composite Materials Test Procedure' (SL235-2012). The specimen is dumbbell-shaped, and the width of the tensile part of the specimen is 6 mm, as shown in Figure 1. The number in the figure is the size of the sample, in mm. The temperature of the laboratory was \(22\pm 2\)\({}^{\circ}\)C and the humidity was 50 \(\pm\) 10%. Before the test, the initial spacing between the two fixtures is adjusted to 100 mm, and the specimen is placed in the middle of the fixture to prevent eccentric force. In the loading process of the specimen, the displacement loading rate of the testing machine is set to 5 mm/min, and the testing machine can obtain the axial force and displacement of the specimen. Two specimens numbered S1 and S2 were prepared using the modified polydimethylsiloxane materials. The thicknesses of the specimens are 1.28 mm and 1.48 mm, respectively. Figure 1: Specim size and photos. (**a**) Specim size (mm). (**b**) Specim. Experiment analysis method  
The nominal stress-strain method is usually used to analyze the test data in the uniaxial tensile test. The stress and strain are calculated according to the following formula:  
\[T=\frac{F}{A} \tag{1}\]  
\[A=t_{0}\times b \tag{2}\]  
\[\varepsilon=\frac{\delta}{\delta_{0}} \tag{3}\]  
where \(T\) is the engineering stress (nominal stress), \(F\) is the force, \(A\) is the cross-sectional area, \(t_{0}\) is the thickness, \(b\) is the width, \(\varepsilon\) is the nominal strain, \(\delta\) is the measured length elongation, and \(\delta_{0}\) is the measurement length. The above formulas do not consider the change in the cross-section and the total length of the specimen during the tensile process when calculating the stress and strain. However, in the actual tensile process, many hyperelastic materials will have a certain necking phenomenon during large deformation. Therefore, on this basis, considering the actual situation, the true stress-strain is calculated by the following formula:  
\[T_{R}=T\times(1+\varepsilon) \tag{4}\]  
\[\varepsilon_{R}=\ln(1+\varepsilon) \tag{5}\]  
where \(T_{R}\) is the true stress and \(\varepsilon_{R}\) is the true strain. (3) Test result analysis  
Uniaxial tensile tests were carried out on the specimens, as shown in Figure 2. The axial force and displacement of the specimens from the beginning of tension to fracture were recorded by the testing machine. The maximum tension and maximum displacement of the two specimens are shown in Table 1.  
From the Formulas (1)-(3), the nominal stress-strain curve of the modified polydimethylsiloxane membrane can be obtained, as shown in Figure 3a. Similarly, the nominal stress and strain can be converted to the true stress and strain by Equations (4) and (5), so as \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Maximum Tension (N)** & **Maximum Displacement (mm)** \\ \hline S1 & 20.544 & 89.953 \\ S2 & 24.326 & 94.152 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Uniaxial tensile test results. Figure 2: Uniaxial tensile test of modified polydimethylsiloxane material. to obtain the true stress-true strain curve of the modified polydimethylsiloxane membrane, as shown in Figure 3b. The stress-strain curves of the S1 and S2 samples are relatively close; therefore, the average value of the two sets of data can be used as the tensile properties of the modified polydimethylsiloxane membrane.