## 3 Results
### Four-Point Bending Test: Experimental Results and Numerical Model Tuning  
Results of the four-point bending tests are here presented. Two undamaged composite plates have been tested until almost complete failure occurred. In particular, the upper layers, which are subjected to compressive loads, showed the most significant failures. Intralaminar cracks propagate in correspondence of the inner span noses. The numerical model is analyzed only in the elastic field and it results in good agreement with the experimental data, as shown in Figure 3. Displacement of the numerical analysis has been evaluated on the rigid cylinders. However, as described in Section 2.2, the rigid wall cylinders are initially distanced from the composite laminate. Consequently, the initial path of the force-displacement curve is characterized by the growing contact between laminate and cylinders, which is not significant for the purpose. The numerical force-displacement curve has been thus shifted leftwards and results of the numerical analysis are reported from 1 mm of displacement. Figure 4 shows a magnification of the cracks, obtained through an optical microscope. The complete failure can be appreciated for the upper four layers. Progressive Damaging and Assessment of Residual Elastic Properties through the DI\({}_{d}\) Technique  
An undamaged composite is subjected to repeated four-point bending tests. Load is increased until incipient failure occurs and then decreased. Achieved failure is not complete, as the load-carrying capacity of the composite laminate is still significant. In total, five repetitions are performed, as shown in Figure 5, where the resulting force-displacement curves are numbered as Test n.1, Test n.2, Test n.3, Test n.4, and Test n.5. As the damage increases, the plate stiffness progressively decreases. Loading and unloading cycles are performed until the residual stiffness of the composite plate is about 40% of the original value. This is shown with the Test n.6 (damaged specimen curve), which is performed only in the elastic field. A significant damage level is thus induced through the five tests. Figure 4: Magnification of intralaminar cracks: failure of the upper four layers. Figure 3: Experimental and numerical results of the four-point bending tests. The \(DI_{d}\) technique is then adopted to estimate the residual elastic properties. Preliminary characterization tests allowed to evaluate the threshold energy \(\varepsilon_{th}\), which is in this case equal to 5 J. Details of the preliminary tests are not discussed here. A complete description of the procedure can be found in [15]. Figure 6 shows the resulting correlation between the residual elastic properties of the analyzed composite and the \(DI_{d}\) parameter. The dotted line is thus adopted to evaluate the residual elastic properties in the progressively damaged plate. Cross markers correspond to the preliminary characterization tests. Figure 5: Progressive damaging of composite plate through four-point bending tests. As reported in Figure 2, the elastic properties have been estimated at seven locations along the middle line of the composite plate. Table 2 reports the measured \(DI_{d}\) values and the corresponding Young's moduli, as well as the locations in x direction of the impacts. In correspondence of the external noses, whereas the bending moment is null in the four-point bending test and no damage should be present, the elastic modulus is equal to 32.8 GPa, which is significantly different from the original value of 54 GPa. This can be justified by taking into account that the circular unclamped region considered for the \(DI_{d}\) test has a diameter of 76 mm. Consequently, elastic properties are assessed as an average of the unclamped region. Further, as clamping boundary conditions have to be realized all around the laminate, the diameter of 76 mm limits the region where the residual properties can be measured through the \(DI_{d}\).