## 8 Conclusions  
In this paper, we have explored the possibility of modeling impact damages as a conical shape geometry with decayed stiffness properties in a homogeneous CFRC plate. This work is mainly motivated by the fact that scattering characteristics of Lamb waves in composites are more complicated than the scattering at defects in isotropic plates. The developed 3-dimensional finite element method allowed to determine the scattering pattern of an incident A\({}_{0}\) Lamb wave in intact and impacted CFRC plates, where the excitation frequency was set below the \(A_{1}\) cut-off frequency. Besides, the numerically predicted scattered displacement fields were compared with the experimental measurements performed on CFRC plates with the same characteristics. A comparison between reconstructed signals from the FE model and experimental measurements allowed us to validate the model and to study the effect of different geometrical configurations (through-thickness depths and diameters of the base) of a conical damaged zone on the scattering diagrams. Results revealed that scattering directivity of the displacement field significantly depends on the depth and width of the conical damage created during the point-impact of the composite. Indeed, on the basis of the results, the scattering amplitude is maximum when the aspect ratio is beyond one and the depth of the impact damage is half the thickness of the composite. However, the detection of impact damage with a small aspect ratio and a relatively small depth (-0.3 or -0.4) seems to be more difficult. The scattering physical insight at the impact-damaged area provided by the above-presented results can be used to optimize the monitoring of composite structures by improving the transducers' location in connection with the involved Lamb mode(s). This work also showed that the study of backward scattering is not always possible. Indeed, results revealed that backward scattering is smaller in amplitude than the forward scattering and its amplitude is only important in the case of a small aspect ratio. Finally, we note that the post-impact damage study performed herein can be extended to include uncertainties related to the structural and mechanical properties of the composite. Indeed, the uncertainties we have taken into account are essentially related to the velocities (position and time of flight). Under the transversely isotropic condition, the optimized elastic constants as well as their uncertainties are determined by fitting the analytic group velocity dispersion curve with the experimental velocities. At the wavelength scale, the considered elastic constants include the average properties of the constituents of the composite as well as the defects therein such as micro-porosities, etc. This can affect the results obtained when the wave propagates in certain directions, especially the case of the composite. Figure 16: Variation of amplitude of scattered A\({}_{0}\) mode with respect to aspect ratio (2 \(\tau\)/\(\lambda\)) towards 45\({}^{\circ}\) direction. cially those where the defects are most present. However, we note that taking uncertainties into account in the modeling is beyond the scope of this work. Indeed, the main objective of this contribution is to study the interaction of the A\({}_{0}\) mode with a conical impact defect. Taking into account uncertainties is extremely expensive, computationally, in view of the large number of required analyses and requires the development of a specific study [46; 47]. Indeed, the complex structure of composites and their manufacturing processes create different sources such as fiber waviness, ply wrinkling, machine tolerance, etc., which can be at the origin of uncertainty [48; 49]. The statistical nature and distribution of imperfections in composites requires therefore the development of simulations, which are able to take into account the complexity of the material and perform calculations in reasonable times [50].