## 3 Validation and Analysis
The results presented in Figure 5a show the numerical values of the impulse on the exposed surfaces of the four-cable ballistic pendulum. The total impulse and experimental measurements are also displayed for comparison. It should be noted that the ALE approach predicts the time of arrival of the wave to be approximately 200 \(\upmu\)s, which coincides with the time of arrival of the blast wave to the first exposed surface (i.e., the rig-front in Figure 2). At almost the same time, the wave impacts the front skin of the sandwich plate; note that only 12 mm separate both surfaces. The remaining exposed surfaces receive the impact of the blast wave instants later. With the LBE approach, only the directly \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Sandwich skin** & **Exp [mm]** & **ALE [mm]** & **Error [\%]** & **LBE [mm]** & **Error [\%]** \\ \hline \multirow{2}{*}{**NL20-10**} & Front & 5.63 & 5.28 & 6.2 & 5.52 & 1.9 \\  & Back & 5.01 & 4.68 & 6.6 & 4.71 & 5.9 \\ \hline \multirow{2}{*}{**NL20-15**} & Front & 5.13 & 5.15 & 0.4 & 5.49 & 7.0 \\  & Back & 5.22 & 4.36 & – & 4.40 & – \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental and numerical displacements to the ballistic pendulum. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Experimental [Ns]** & **ALE [Ns]** & **Error [\%]** & **Load Blast Enhanced (LBE) [Ns]** & **Error [\%]** \\ \hline
**NL20-10** & 15.87 & 16.98 & 7.0 & 17.84 & 12.4 \\
**NL20-15** & 15.85 & 16.26 & 2.6 & 17.89 & 12.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental and numerical impulses transmitted to the ballistic pendulum. exposed surfaces of the rig and sandwich plate receive impulse--all other surfaces are shadowed by these, as shown in Figure 5. The main contribution to the total impulse is the one on the directly exposed surfaces and, thus, the LBE method is capable of accurately predicting the transmitted impulse. A similar analysis and conclusion can be drawn from the evolution of the impulse on the NL20-15 sandwich plate. The ALE and the LBE approaches both predict a higher impulse on the frontal surface of the rig than on the sandwich. Although the rig is not in the direct line of the blast wave, it has a higher exposed surface--53% more than the sandwich plate specimen--which leads to a higher transmitted impulse. However, the pressure is higher on the surface of the sandwich panel as the blast wave hits it orthogonally. This is shown in Figure 4(b). The numerical model using the LBE method shows higher pressure on the sandwich, which is a likely explanation for the higher observed deflections, as listed in Table 6. However, it should be noted that the pressure pulse shape is similar with both numerical approaches. The sudden increase of the impulse at approximately 0.2 ms is consistent with the time of arrival of the blast wave and it is recorded similarly in both approaches. However, the LBE method predicts a constant value of impulse afterwards, while the ALE method shows impulse fluctuations. These differences are caused by (i) a misrepresentation of the negative phase of the blast wave by the LBE approach, as shown in Figure 4(b), and (ii) blast wave reflections on other surfaces, an effect that can only be reproduced by the ALE model. Figure 5: Impulse and pressure-time histories for NL20-10 specimen in LBE numerical model. However, the LBE method predicts a constant value of impulse, while the ALE method shows impulse fluctuations. This is caused by (i) a misrepresentation of the negative phase of the blast wave by the LBE approach, as shown in Figure 5, (ii) blast wave reflections on secondary surfaces, an effect that can only be reproduced by the ALE model, and (iii) blast wave clearing effects. The fluctuations on the impulse on the shadowed surfaces calculated with the ALE approach and shown in Figure 5a, can be explained through an incremental analysis of the interaction of the blast wave with the pendulum.