## 5 3D FE Model and Schematic of the Problem
According to this configuration, the schematics of the laboratory experiment are shown in Figure 7. Since the frequency of the incident Lamb wave mode is chosen below the A\({}_{1}\) cut-off, \(\lambda_{MAX}\) is the wavelength of the S\({}_{0}\) mode at the frequency of interest. Figure 5: Schematic of the 3D-finite element model. the size of the AR is considered equal to 87 mm (\(\approx\)1.5 \(\times\) 57.7) all around the four sides of the 3D-FE model. Interaction of A\({}_{0}\) Mode with Impact Damage and Comparison between Numerical Predictions and Experiment  
To compute the scattered displacement field of the incident A\({}_{0}\) mode sent towards the impacted zone, two different 3D-FE models are developed. At first, a 3D-FE model, taken as a reference, consisting of an undamaged plate, is solved to compute the incident wave field corresponding to the A\({}_{0}\) mode. The second 3D FE model, which takes into account the conical defect representing impact damage, is solved to compute the total wave field of the incident A\({}_{0}\) mode. The incident field computed from the first model is then subtracted from the total wave field computed from the second model to obtain the complex scattered wave field of incident A\({}_{0}\) mode. In both undamaged and damaged cases, the dimensions of 3D-FE models are equal to 300 mm \(\times\) 300 mm \(\times\) 6.2 mm. The excitation of the pure A\({}_{0}\) mode is achieved by giving the unit norm\({}_{1}\) stress at a single frequency (in out of phase manner) using two circular regions, with diameters equal to 13 mm, placed on the opposite sides of the plate and centered at points (110, 0, 110) and (110, 6.2, 110) as shown in Figure 6. The reference model contains 724,365 tetrahedral mesh elements with 3,132,252 degrees of freedom that makes at least four elements per wavelength along the thickness of the plate and at least four elements along the \(XZ\) plane insuring good convergence and accuracy of the FE solution. For the validation of the FE model with the experiment, the model is first solved for a Gaussian profile sinusoidal signal with seven cycles centered at a frequency of 100 kHz by inserting its respective complex Fourier amplitudes as normal stresses on both sides of the plate for 63 different frequencies running between 76 kHz and 123 kHz. After solving the FE model using a linear solver with Lagrange quadratic elements and applying Neumann boundary conditions, the excitation and reception of signals are performed using the inverse Fourier transform of the normal components of the displacement at (110, 6.2, 110) and (210, 6.2, 210), respectively. These two points are separated by a distance of 142 mm. The reconstructed signals of excitation and reception predicted by the FE model are shown in red in Figure 8. Some angular signals around the center at (150, 6.2, 150) are also reconstructed and are shown in Figure 9. The latter figure shows that the amplitude at 225\({}^{\circ}\) is the highest and that the ones corresponding to the symmetrical positions at (180\({}^{\circ}\) and 270\({}^{\circ}\)) and (0\({}^{\circ}\) and 90\({}^{\circ}\)) have lower amplitudes and are equivalent. Since our study only deals with the scattering of amplitude, all 3D-FE models are solved for a single excitation frequency of 100 kHz to save computation time and cost. The amplitude of the incident A\({}_{0}\) mode, i.e., the normal component of the displacement vector '\(v_{incl}\)', is monitored at the mid plane (at y = 3.1 mm), where 360 positions around a circle centered at (150, 3.1, 150) with a radius equal to 20 mm are considered.