## 3 Finite Element Simulation Analysis of Electromagnetic Field  
### Model Establishment  
In order to investigate the electromagnetic coupling between the sensors and CFRP materials, we utilized the COMSOL6.1 software package (Stockholm, Sweden) to establish an FEM simulation model. The simulation geometric model is depicted in Figure 1 (the air domain is not shown in the figure). Four identical coils form an excitation coil group in the same plane. The current in the adjacent coils is of equal magnitude but flows in the opposite direction, causing these four coils to form an 8-shaped structure in pairs. Its top view is presented in Figure 2. The total magnetic flux generated by the excitation coils within the area of point a, which is located on the perpendicular bisector of the center connection lines of coil 1, coil 3, and coil 2, coil 4, is zero. That is, under this design, the magnetic field generated by the excitation coils does not have an impact on the detection coils [12]. The detection coil is placed above the center point of the excitation coil group and is enlarged to cover the plane of the tested CFRP prepreg sample. The parameters of the coils and the carbon fiber test material are listed in Table 1.  
Figure 1: Simulation model illustration depicting four T_coils, one R_coil, and a CFRP model.  
In the AC/DC module of the COMSOL6.1 software, the physical field is selected as the magnetic field and solved in the frequency domain. The relative magnetic permeability and relative dielectric constant of this model are both set to 1. The conductivity of the air domain is set to 1 S/m, which simplifies the model and reduces the computational complexity without exerting a significant influence on the results. The excitation coil and the receiving coil are set to copper, with the conductivity set at 5.998 MS/m. The conductivity of the carbon fiber composite material varies in each direction, presenting a distinct electrical anisotropy, and its conductivity is represented by the conductivity tensor Equation (2), where \((\sigma_{L},\sigma_{T},\sigma_{cp})\) = (5000, 200, 50) S/m. The meshing of the geometric model is depicted in Figure 3. The coil domain and CFRP domain are meshed using adaptive meshing, where the meshing becomes increasingly dense until the change in energy is below the predefined value (e.g., 0.1%) [18], while the air domain is meshed with refined tetrahedral meshes. A 1A quadrupolar current is passed through the excitation coil, inducing eddy currents in the CFRP prepreg. The number of nodes is approximately 250,000. The magnetic field produced by the eddy currents leads to variations in the magnetic flux in the detection coil, based on which the material properties of the CFRP prepreg can be deduced.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Geometric Parameters** & **Values** \\ \hline Inner diameter of the T-coil & 10 (mm) \\ Outside diameter of the T-coil & 30 (mm) \\ Height of the T-coil & 1 (mm) \\ Number of turns of the T-coil & 50 \\ Inner diameter of the R-coil & 30 (mm) \\ Outside diameter of the R-coil & 110 (mm) \\ Height of the R-coil & 1 (mm) \\ Number of turns of the R-coil & 100 \\ The distance between neighboring transmit coil centers & 50 (mm) \\ Detachment distance & 5 (mm) \\ Plate volume & 50 \(\times\) 50 \(\times\) 2 (mm) \\ Air domain volume & 1000 \(\times\) 1000 \(\times\) 1000 (mm) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of coils and carbon fiber materials.  
Figure 2: Top view of quadrupolar structure. O1–O4 denote the centers of the four transmitting coils and the arrows indicate the current directions.