# Experimental and Numerical Evaluation of Calcium-Silicate-Based Mineral Foam for Blast Mitigation
## 4 Results from Simulations
### Parametric Study  
#### 4.3.1 Influence of the Core Configuration  
As shown in the experimental results in Section 2.4.3, the effectiveness of the SC is influenced by the core geometry. By increasing the \(\zeta\) value from configuration A to C, the maximum deflection of the backplate is decreased. Therefore, three extra configurations (D to F) with higher values of \(\zeta\) are included in this study. The effectiveness of each solution is assessed based on reductions in maximum OPD at the backplate's center, mean permanent deformation and the absorbed energy by the foam. Figures 20 and 21 present the maximum deflection and mean permanent deformation at the backplate's center. Contrary to the findings of [PERSON] et al. [42], this study does not reveal any negative protection effects of the SC. Adding a foam layer consistently decreases maximum deflection and mean permanent deformation for all the considered configurations. Regardless of the charge mass, the minimum reduction in terms of maximum deflection and mean permanent deformation at the center is about 30% obtained with configuration F. In comparison, the maximum reduction is about 60 and 70%, respectively, obtained with configuration C. Figures 22 and 23 highlight an optimal value of \(\zeta\) (corresponding to configuration C) that minimizes deflection while maximizing the absorbed energy by the foam. This optimal value remains even with higher explosive charge masses. To gain further insight into the underlying phenomena, an analysis of the deformation of the backplate and front skin, and crushing level of the foam is performed in Figures 24-27. The curves in Figure 26 corresponding to the crushing level of the foam are obtained using Equation (2):  
\[\text{crushing level}=1-\frac{\delta_{\text{BP}}\left[\text{mm}\right]- \delta_{\text{FS}}\left[\text{mm}\right]}{60\,\text{mm}}, \tag{3}\]  
Figure 19: Experimental and numerical deflection profiles: (**a**) Without the protective foam, (**b**) Configuration A, (**c**) Configuration B, and (**d**) Configuration C.  
where \(\delta_{buckplate}\) is the deformation of the backplate, \(\delta_{front\ skin}\) is the deformation of the front skin, and 60 is the thickness of the foam (see Figure 25). A crushing level of 1 means that the foam has reached full densification. Figure 21: Bar chart illustrating the mean permanent deformation of the backplate’s center across various configurations and three charge masses. Figure 22: Maximum deflection at the backplate’s center as a function of \(\zeta\) and for different explosive charge masses. Figure 23: Absorbed energy by the foam as a function of \(\zeta\) and for different explosive charge masses. Figure 24: Isometric view of the out-of-plane displacements (in mm) of the backplate (top plate), foam and front skin of the different configurations. Figure 25: Deflection profiles at mid-plane of the backplate and the front skin. Figure 24 provides an isometric view of the OPD of the backplate (top plate), foam and front skin for the considered configurations at the maximum values. Configuration C demonstrates less than 2% of the area with displacement values exceeding 12 mm and 65% of the area below 6 mm. Furthermore, the entire front skin has moved more than 54 mm. This means the foam has nearly reached full densification, as shown in Figure 26. It must be highlighted that foam crushing is relatively uniform from configuration A to C.  
Figure 27 illustrates the out-of-plane displacement evolution up to 0.6 ms of the backplate, foam and front skin for configurations C, D, and E. Configurations C and D exhibit a similar architectural layout, differing primarily in the size of the foam core, which is smaller in configuration D compared to configuration C. Research by [PERSON] et al. [33] demonstrates that the size of the foam sample influences its plateau stress.