## 5 3D FE Model and Schematic of the Problem
The center position corresponding to excitation and the center of the monitoring circle causes an incident angle of 225\({}^{\circ}\) in such an arrangement of the sensors as shown earlier in Figure 6. The numerically computed normalized incident field in the absolute value (shown in solid line) is shown in Figure 10. In the second FE model (damaged case), impact damage is introduced as a right circular cone with a diameter of 30 mm and a depth of 5.2 mm eep, with 80% decayed material stiffness. The top tip of the conical geometry is situated at (150, 6.2, 150) and at a depth reaching 5.2 mm through the thickness of the plate. In the presence of impact damage, the 3D-FE model contains 794,937 tetrahedral mesh elements in total with 3,419,892 degrees of freedom. The maximum mesh element size inside and around the impact zone is set to 1 mm while the remaining area is set to be at least 4 mm per wavelength. The model is solved for the same incident frequency of 100 kHz using the same linear solver with Lagrange quadratic elements and applying Neumann boundary conditions. The total field (i.e., the normal component of the displacement vector '\(v_{tot}\)') from the 3D-FE model is monitored at the mid plane around the same circular path at 360 positions at a distance of 20 mm from the center of the damaged zone. The numerically calculated normalized total field in absolute value (shown in solid line) is shown in Figure 11. The amplitude of the scattered A\({}_{0}\) wave '\(v_{scat}\)' around the impacted zone is calculated as the absolute difference of the complex magnitudes (\(v_{scat}=\left|\,v_{tot}-v_{inc}\,\right|\)) at each point between the reference and the damaged state for all 360 monitored points around the circle. The normalized absolute difference of the scattered \(A_{0}\) mode is shown in Figure 12.  
Figure 7.0 Comparison between reconstructed signal from the FE model and experimental measurements for two positions 142 mm apart. Figure 7.1 Reconstructed signal from the FE model at some angular positions 20 mm away from the center of impact damage. Figure 7.2 Experimental measurements (dashed) and numerical predictions (solid) of the total displacement field of A\({}_{0}\) mode propagating in the impacted CFRC plate. Figure 7.3 Experimental measurements and numerical predictions of the incident A\({}_{0}\) mode propagating in the intact CFRC plate. The laboratory experimental setup (shown in Figure 7) for measuring the incident and total fields of the incident A\({}_{0}\) mode includes the same Gaussian profile sinusoidal signal with seven cycles centered at a frequency of 100 kHz (the same as that used in the FE model) where excitation and reception are performed via two identical transducers (PanametricsTM V106). Acoustic field amplitudes are monitored at 32 different positions around the circle for intact and damaged plates. A LabviewTM code is programmed along with MatlabTM to store and process the experimental measurements. The transmitter is attached to the composite plate with the help of a thermal resin. It is very difficult to generate a pure A\({}_{0}\) mode in the laboratory. Indeed, when a pulse is sent towards the transmitter to generate the A\({}_{0}\) mode, a small portion of the S\({}_{0}\) mode (shown inside the dotted circle in Figure 8) is also being excited. With S\({}_{0}\) being three times faster than A\({}_{0}\), one can easily choose the propagating distance to avoid any overlapping between the generated modes. Furthermore, the ratio of amplitudes between S\({}_{0}\) to A\({}_{0}\) is around 4%, which suggests neglecting the S\({}_{0}\) contribution, in accordance with the literature [25]. Therefore, the received mode will be almost a pure A\({}_{0}\) mode with negligible interference of the S\({}_{0}\) mode.