## 3 Finite Element Modeling and Probe Parameter Determination  
### Finite Element Model  
In order to determine the parameters of the designed probe and validate its performance, this study utilizes COMSOL Multiphysics. Within the AC/DC module, the magnetic field was chosen as the physical field to establish a three-dimensional model for the novel embedded triple rectangular array probe detecting CFRP. Figure 4 shows the geometric model, which consists of three parts: the outermost rectangular air domain, the novel triple rectangular coil probe, and the CFRP sample. The geometric dimensions of the rectangular air domain are 300 mm \(\times\) 300 mm \(\times\) 100 mm. Figure 5 depicts the CFRP sample, which is composed of 16 layers of orthogonally laid carbon fiber composite material. The dimensions of the sample are 150 mm \(\times\) 100 mm \(\times\) 4 mm, with each layer having a thickness of 0.25 mm. The layup direction is [0\({}^{\circ}\)/90\({}^{\circ}\)]\({}_{8}\). The electrical conductivity of CFRP exhibits significant anisotropy, meaning it has different conductivities in different directions. The conductivity tensor includes longitudinal conductivity (the fiber direction), transverse conductivity (perpendicular to the fiber direction), and interlayer conductivity. Specifically, the longitudinal conductivity (\(\sigma_{\text{L}}\)) is typically between 5000 S/m and 50,000 S/m, the transverse conductivity (\(\sigma_{\text{T}}\)) is between  
Figure 4: Geometric model. Figure 5: CFRP sample. 10 S/m and 100 S/m, and the interlayer conductivity (\(\sigma_{\rm cp}\)) is between 10 S/m and 100 S/m. It is generally considered that the interlayer conductivity is half of the transverse conductivity [29]. In the modeling, classic conductivity values (\(\sigma_{\rm L}\), \(\sigma_{\rm T}\), \(\sigma_{\rm cp}\)) = (10,000, 100, 50) S/m were assigned to the CFRP. In the magnetic field, apart from electrical conductivity, other major material properties include relative magnetic permeability and relative permittivity. In this model, both relative magnetic permeability and relative permittivity are set to 1. The material for the coils is copper, with an electrical conductivity of 5.998 \(\times\) 10\({}^{7}\) S/m. The conductivity of delamination and air is 0 S/m. To balance computation accuracy and the computational capacity of the computer, different division methods are applied to various sections of the model. The air domain of the model is divided using refined tetrahedral mesh elements. The CFRP sample and the probe are divided using finer hexahedral mesh elements. The delamination part, which has the most significant impact on the solution results, is divided using highly refined hexahedral mesh elements. The boundary between the delamination and CFRP is divided using refined triangular mesh elements. After completing the mesh division, this model generates a total of 188,299 domain elements, 19,944 edge elements, and 160 vertex elements. The mesh partition of the simulation model is shown in Figure 6.  
The equation for calculating the skin depth of the CFRP sample with an orthogonally orientation [\(0^{\circ}/90^{\circ}\)]\({}_{8}\) is [30]:  
\[\delta=2\sqrt{\frac{1}{\mu_{0}\sigma_{\rm L}\omega}}, \tag{9}\]  
where \(\omega\) is the angular frequency, \(\mu_{0}\) is the material's permeability, and \(\sigma_{\rm L}\) is the fiber direction conductivity. The thickness of the sample in Figure 5 is 4 mm. According to Equation (9), the excitation frequency is determined to be 1 MHz. At this frequency, the skin depth is 7.1 mm, and eddy currents can penetrate to the bottom of the sample without significant attenuation. This is advantageous for detecting subsurface defects located deeper within the sample. Hence, in the simulation experiment, a sinusoidal current with a frequency of 1 MHz and amplitude of 1 A, in opposite directions, is applied to the two excitation coils.