## 5 3D FE Model and Schematic of the Problem
A comparison between the reconstructed signals from the FE model and the experimental measurements (shown in red color) for same distance of 142 mm is shown in Figure 7.4 Indeed, by considering 12% attenuation into the 3D-FE model, the simulated amplitudes are found to be in good agreement with the experimental amplitudes for the A\({}_{0}\) mode. We also note a difference in simulated and experimental signals between \(\sim\)225 \(\upmu\)s and \(\sim\)250 \(\upmu\)s. The latter could be a consequence of the homogenization of the elastic properties corresponding to the different layers of the composite, which appears more clearly in the case of small wavelengths i.e., A\({}_{0}\) mode. However, these minor discrepancies have a very limited effect on the estimation of the amplitude of the A\({}_{0}\) mode as it can be observed in Figure 7.5 For the undamaged plate, the measured incident amplitudes (blue circles) are normalized and compared with the simulated normalized incident amplitudes (solid line) as shown in Figure 7.6 The latter shows that the scattered field remains symmetrical in terms of directivity and amplitude with respect to the direction 225\({}^{\circ}\). For the damaged plate, the total displacement field is measured at the same 32 points to make the comparison possible. The normalized measured amplitude of the total field (blue circles) and simulated total field amplitudes (solid line) are shown in Figure 7.7 The directivity behavior of the measured total displacement fields is similar to simulations using the 3D-FE model. The A\({}_{0}\) scattered wavefield clearly shows the impact-induced damage area where the amplitude in the damaged area is considerably  
Figure 7.8 Directivity pattern of the scattered field of the A\({}_{0}\) mode deduced from total displacement fields on intact and damaged CFRC plates (See Figures 10 and 11). higher than in the intact area. Furthermore, the A\({}_{0}\) scattered wavefield is also direction dependent. The existing slight difference between simulated and measured total fields may be due to the considered geometrical and stiffness properties of the damaged zone in the 3D-FE model, which can be slightly different from the ones of the real impacted plate. However, one should note that the small discrepancy in the forward directions between simulated and experimental data has already been observed and was attributed to bonding considerations between the layers [14]. Nevertheless, the symmetry of the directivity along 45\({}^{\circ}\)-225\({}^{\circ}\) in measured total field amplitudes reinforces the hypothesis of a homogeneous distribution of the elastic properties as predicted numerically inside the conical damage. Furthermore, the scattered field is obtained by considering the absolute difference between the total and the incident wave fields. The numerically calculated normalized amplitude of scattered A\({}_{0}\) is shown in Figure 7.9 It is noted that the maximum scattered amplitude is towards the 45\({}^{\circ}\) direction i.e., in the direction of the incident A\({}_{0}\) mode. It is also found that there exist two positions near 30\({}^{\circ}\) and 60\({}^{\circ}\), where the amplitude of the scattered A\({}_{0}\) mode is very small as compared to the 45\({}^{\circ}\) direction. The scattered field is symmetric along the 225\({}^{\circ}\)-45\({}^{\circ}\) direction, which corresponds to the direction of the wave vector of the generated guided wave.