## 3 Finite Element Modeling (FEM) of Human-Seat Interactions
### _Material Modeling and Challenges_
#### 3.3.3 Material Modeling for Latex and Fabric Adhesive Tape
The stress-strain behavior of the latex membrane was described using the Ogden model:  
\[W=\sum_{n=1}^{N}\frac{\mu_{n}}{\alpha_{n}}\big{[}(\lambda_{1}^{\alpha_{n}}+ \lambda_{2}^{\alpha_{n}}+\lambda_{3}^{\alpha_{n}})-3\big{]}+4.5K\big{(}J^{ \frac{1}{3}}-1\big{)}^{2} \tag{9}\]  
where \(\mu_{n}\)and \(\alpha_{n}\) are material constants; \(K\) is the initial bulk modulus; and \(J\) is the volumetric ratio, defined as \(J=\lambda_{1}^{2}\lambda_{2}^{2}\lambda_{3}^{2}\). According to the summary by [PERSON] [29], considering the material as incompressible (J = 1) and employing the Ogden model for latex, a 3-term formulation can be applied. For the biaxial mode, the engineering stress-strain curve uses the engineering strain parameters defined as \(\lambda_{1}=\lambda_{2}=\lambda,\lambda_{3}=\lambda^{-2}\). The analysis process to determine the appropriate material model and simulate the experiment, as described above, for the latex membrane was carried out similarly to that for polyurethane foam. This process utilized input data from the strain-stress curve and finite element modeling to simulate the circular membrane inflation test (Figure 10a). Additionally, Figure 10b highlights the significant swelling behavior of the latex tube under 25 kPa internal pressure, underscoring the necessity of fabric tape reinforcement to stabilize the structure. Similar to the analysis process for PU foam, the purpose of this process was to compare the stress-strain curves obtained from the experimental data and simulations, thereby demonstrating that the chosen material model for latex was appropriate. The comparison results are presented in Figure 10c. Figure 10: (**a**) Simulation results for the inflation test of a circular membrane, showing displacement in the z-direction [m]; (**b**) Simulation of the deformation behavior of the latex tube; (**c**) Comparison of experimental stress–strain data (blue) and fitted curves (red) for the latex membrane. With the selected material model being Ogden and the numerical values for the coefficients in Equation (9) set as \(N=3\), the results obtained were:  
\[ \begin{array}{l}\mu_{1}=1.21738\times 10^{8}\text{Pa},\mu_{2}=7.7123\times 10^{6} \text{Pa},\mu_{3}=117.45\text{Pa},\\ \alpha_{1}=0.0110147,\alpha_{2}=0.0123274,\alpha_{3}=15.898,\\ K=3.5946\times 10^{9}\end{array} \]  
The simulation results for the latex tube subjected to 25 kPa internal pressure (Figure 10b) closely matched the experimental data. Figure 10b illustrates the significant swelling capability of the latex tube under an internal pressure of 25 kPa. This highlights the necessity of using fabric tape to wrap the latex tube in order to mitigate this characteristic. Material Characterization of Fabric Adhesive Tape Using Uniaxial Tensile Test  
To ensure the stability of the pneumatic spring, a fabric adhesive tape was wrapped around the latex membrane. The tape's mechanical properties were determined through uniaxial tensile tests, using specimens measuring 0.16 mm in thickness, 48 mm in width, and 220 mm in length. The flow-stress curve obtained from the tests were modeled using the Mooney-Rivlin hyperelastic equation:  
\[W=C_{10}(I_{1}-3)+C_{01}(I_{2}-3)+C_{11}(I_{1}-3)(I_{2}-3)+C_{20}(I_{1}-3)^{2} \tag{10}\]  
For uniaxial extension, the engineering strains are defined as shown in [30] with \(\lambda_{1}=\lambda,\lambda_{2}=\lambda_{3}=\lambda^{-2}\)[25], leading to:  
\[I_{1}=\lambda^{2}+\frac{2}{\lambda},\ I_{2}=2\lambda+\frac{2}{\lambda^{2}} \tag{11}\]  
The material fitting results based on this model were provided as follows: \(C_{10}=-2.55107\times 10^{8},C_{10}=2.9003\times 10^{8},C_{11}=1.18362\times 1 0^{8},C_{20}=-8.66098\times 10^{8}\). The experimental and simulated stress-strain relationships (Figure 11) showed significant alignment, confirming the reliability of the material model for the fabric tape. Figure 11 includes details on the uniaxial tensile testing setup (Figure 11a) and a direct comparison of the experimental (blue) and fitted (red) stress-strain curves (Figure 11b).