## 3 Results and Discussion
### EMI SE Computational Analysis
The frequency domain interface can be written in the form,  
\[\
abla\times\mu_{r}^{-1}\ (\
abla\times E)-k_{0}^{2}n^{2}E=0 \tag{11}\]  
where \(n^{2}=\left(\varepsilon_{r}-\frac{j\sigma}{\omega\varepsilon_{0}}\right)\), where \(n\) is the refractive index, and the wave number of free space \(\mathbf{k}_{0}\) is defined as  
\[k_{0}=\omega\sqrt{\varepsilon_{0}}\mu_{0}=\omega/c_{0} \tag{12}\]  
and the computation of wave through both antennas (transmitter and receiver) can be defined from the below equations,  
\[\text{for port 1},\ S=\frac{f_{\partial\Omega}(E-E_{1}).E_{1}}{f_{\partial \Omega}E_{1}.E_{1}} \tag{13}\]  
\[\text{for port 2},\ S=\frac{f_{\partial\Omega}E.E_{2}}{f_{\partial\Omega}E_{2}.E _{2}} \tag{14}\]  
where \(\omega\) is the angular frequency, \(\sigma\) is the electrical conductivity, \(S\) is the scattering parameter, \(f_{\partial\Omega}\) is the frequency domain, \(\varepsilon_{0}\) and \(\mu_{0}\) are the free space permittivity and permeability, and \(\varepsilon_{r}\) and \(\mu_{r}\) are the relative permittivity and permeability, respectively, and \(c_{0}\) is the speed of light in vacuum [45]. The simplified geometry of flexible bio-based polyurethane foam of size 12 \(\times\) 12 \(\times\) 2 cm was imported in COMSOL Multiphysics using CAD import module capabilities. A unit cell was then built around the imported geometry applying Floquet-periodic boundary conditions on its four sides, creating an infinite 3D array of simplified cellular structures that act like the original model of the bio-based polyurethane foam. Figure 9 shows one port on the bottom face and another on the upper faces of the unit cell to reassemble the experimental conditions described in the Methodology section. Ports 1 and 2 emulate the transmitter and the receiver antenna, respectively. The distance between ports was 42 cm. The imported simplified foam model was placed between Port 1 and Port 2. The electric mode field amplitude in Port 1 was configured following the relation, and their values are permittivity = 1.126 \(\times\) 10\({}^{-11}\) F/m, permeability = 1.257 \(\times\) 10\({}^{-6}\) H/m, and electrical conductivity = 3.588 \(\times\) 10\({}^{-14}\) S/m, where the waveguide width parameter is equal to 2.5 cm. The elevation angle of incidence is 0, which means the electric field is normal to the geometry surface. The mathematical equation for component y of the electric mode field amplitude matches the spatial propagation behavior exhibited by a classic pyramidal horn antenna. The material chosen for the polymeric foam was (built-in) polyurethane, and the domain outside and inside (the bubbles of) the cellular structure was filled with air. The electric and magnetic material properties are required to solve the governing equations of the mathematical model. The frequencies analyzed (parametric sweep) went from 8 GHz to 12 GHz, with a 500 MHz interval between computed values. The norm of the electric field and power flow at 10 GHz are shown in  
Figure 9: 3-D model for analyzing electric field intensity. Figure 10, respectively. Finally, the shielding effectiveness values were computed for each frequency analyzed for the physical model-simulated and the flexible bio-based PU foam. These scenarios are summarized in frequency spectra, as shown in Figure 11. The results carry a relative error of 2.48% between the EMI SE of the manufactured material, which peaked at 28.03 dB, while the maximum value reached for the simulated model is near 27.35 dB.