## 2 Materials and Methods
### Experimental Tests  
Four-point bending tests are performed on two different composite plates until complete failure occurs. The elastic field of the composite plates is thus identified. The tests are performed on a servohydraulic testing machine (Instron 8801). In agreement with the recommendations of ASTM standard D6272 for four-point bending test of reinforced plastics [22], the load span is one third of the support span. As shown in Figure 1, the loading noses are 50 mm distant. The support noses are consequently placed at a distance of 150 mm. Figure 1a shows the experimental setup. The resulting experimental curves of force with respect to displacement are exploited to tune a finite element model of the laminate subjected to four-point bending test, which is shown in Figure 1b. The same experimental setup is adopted to progressively damage an undamaged composite plate. The plate is loaded until incipient failure occurs and then unloaded. The repeated four-point bending tests progressively reduce plate stiffness. A significant damage level is thus induced. In order to assess the residual Young's modulus of the damaged plate, the detecting Damage Index (\(DI_{d}\)) technique is adopted. The \(DI_{d}\) methodology consists of two sets of experimental tests. Firstly, a preliminary characterization activity is performed, which allows to identify the correlation between \begin{table}
\begin{tabular}{c c} \hline
**Property** & **Value** \\ \hline Density & 1.45 10\({}^{3}\) g/cm\({}^{3}\) \\ Young’s modulus in longitudinal and transverse direction (\(E_{1}=E_{2}\)) & 54 GPa \\ Shear modulus (\(G_{12}\)) & 3.5 GPa \\ Poisson’s ratio (\(\
u_{12}=\
u_{21}\)) & 0.08 \\ \hline \end{tabular}
\end{table} 
Table 1: Material properties. Figure 1: Four-point bending test: (**a**) experimental setup; (**b**) numerical model. residual elastic properties and the \(DI_{d}\) parameter. Then, the investigated component undergoes the non-destructive test in order to estimate the local residual elastic properties from the \(DI_{d}\). In particular, the methodology is based on two sets of impact tests: the first intends to damage the material at increasing impact energy levels and allows to evaluate the so-called threshold energy \(\varepsilon_{th}\). The threshold energy is defined as the impact energy at which the reduction of local elastic properties is less than 5%. An impact at the threshold energy can be considered as non-destructive for the material. The second set of impacts is performed at the threshold energy and allows to evaluate the residual elastic properties. In this work, the first series of impacts were performed on a set of plates made of the same composite fabric. The impact tests were carried out using a free-fall drop dart testing machine (CEAST 9350 FRACTOVIS PLUS). Clamping boundary conditions were realized through a mechanical clamping system which applies an almost uniform pressure on the clamped area. A circular unclamped region of diameter 76 mm was considered for the tests, in agreement with the recommendations of ASTM standard D5628 [23]. The impact energy was defined by varying the impactor mass for a given impact velocity. The impact velocity, which was controlled by the drop height of the dart, was measured in each test with an optoelectronic device. A piezoelectric load cell, mounted in proximity of the tip of the impact dart, acquired the force signal at a sample rate of 1 MHz. The second series of impacts, which are carried out at the threshold energy, is performed on the plate previously damaged with the repeated four-point bending tests. In particular, damaged plate is impacted along the middle line. Moving along the longitudinal direction of the plate (x direction of Figure 1), the impacts are located in correspondence of the external noses, in the regions where bending moment is linearly increasing, in correspondence of the internal noses and finally in the middle of the load span.