# Delamination Assessment in Composite Laminates through Local Impulse Excitation Technique (IET)
## 3 Results
### The Identification of the FE Model of the Local-IET Test  
To replicate the local-IET test in the FE simulation environment, the stiffness of the springs was determined, such as the sum of the first resonant frequency of the FE model, and the intercept (120.5 Hz) matches the experimentally measured frequencies presented in the previous section. Table 2 reports the resulting stiffness of the FE model with translational springs and rotational springs. For the rotational springs model, the stiffness very slightly varied with the size of the device, and therefore, a unique mean value was considered. Nevertheless, the discrepancy between the experimentally measured frequencies and those calculated using the FE model was always lower than 5%. According to Table 2, the stiffness of the springs varies with the material elasticity and the size of the device in accordance with the previous observations. In this regard, we can consider that the higher the discrepancy between the displacements in the center and at the extremities of the device, the more the boundary conditions approximate the ideal clamping in accordance with the modal shape of the clamped solution. As such, the higher the material elasticity, the more comparable the displacements in the center and at the extremities, and the stiffness of the springs must decrease. Equivalently, the thinner the plate, the more the difference in displacements at the center and at the extremities, and the stiffness of the springs must increase to constrain the displacement in proximity to the extremities and resemble the perfectly clamped boundary conditions. In order to identify the FE model that better replicates the local-IET tests, a comparison between the experimental and numerical modal displacements of the first mode was performed. The same measurement line inspected in the experimental investigations was extracted from the FE model. Figure 8 shows the comparison of the experimental and numerical modal displacements in the case of the plain weave plate and 150 \(\times\) 150 mm device. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Size of the Device [mm]** & **First Resonant Frequency [Hz]** & **k\({}_{\text{translational}}\)** & **k\({}_{\text{rotational}}\)** \\  & **Device [mm]** & **Frequency [Hz]** & **[N/mm]** & **[N -mm/rad]** \\ \hline \multirow{3}{*}{UD MAT\#1} & \(150\times 150\) & 436 & 0.41 & \\  & \(100\times 100\) & 810 & 1.28 & \\  & \(75\times 75\) & 1315 & 2.86 & \\  & \(50\times 50\) & 2617 & 7.95 & \\ \hline \multirow{3}{*}{Plain Weave MAT\#2} & \(150\times 150\) & 385 & 0.26 & \\  & \(100\times 100\) & 719 & 0.89 & \\  & \(75\times 75\) & 1177 & 2.05 & \\  & \(50\times 50\) & 2418 & 6.16 & \\ \hline \multirow{3}{*}{Twill 2 \(\times\) 2 carbon fiber MAT\#3} & \(150\times 150\) & 615 & 1.48 & \\  & \(100\times 100\) & 1150 & 3.89 & \\ \cline{1-1}  & \(75\times 75\) & 1847 & 7.84 & \\ \cline{1-1}  & \(50\times 50\) & 3258 & 15.22 & \\ \hline \multirow{3}{*}{Twill 2 \(\times\) 2 glass fiber MAT\#3} & \(150\times 150\) & 500 & 1.37 & \\ \cline{1-1}  & \(100\times 100\) & 890 & 3.24 & \\ \cline{1-1}  & \(75\times 75\) & 1425 & 6.72 & \\ \cline{1-1}  & \(50\times 50\) & 2720 & 16.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resulting stiffnesses for FE model with translational and rotational springs. For a consistent comparison, the modal displacements were normalized. As shown in Figure 8, although both models are in good agreement with the experimental data, the rotational springs model better predicts the vibrational response of the plate in correspondence with the boundaries, where the translational springs model shows a lower slope with respect to the experimental results. A similar conclusion can be achieved by comparing the experimental and numerical modal displacements of the unidirectional plate. Given the remarkable orthotropy of the material, the modal displacement was acquired along both the longitudinal and transverse directions.