# Experimental and Numerical Evaluation of Calcium-Silicate-Based Mineral Foam for Blast Mitigation
## 2 Air-Blast Experiments
### Experimental Set-Up  
The experimental set-up shown in Figure 1a is used to investigate the absorption capacity of the calcium-silicate-based mineral foam. It comprises a rigid frame made from steel measuring 1000 \(\times\) 1000 \(\times\) 15 mm\({}^{3}\), featuring a central square opening of 300 \(\times\) 300 mm\({}^{2}\). Within this frame, a square aluminum plate sample (Figure 1b), measuring 400 \(\times\) 400 mm\({}^{2}\) with a thickness of 2 mm, is securely clamped. By using bolted connections and a clamping frame (Figure 2a), clamping is achieved to establish fixed boundary conditions. A wrench is used to tighten the bolts, applying a torque of 100 Nm. Following the recommendation for M12 bolts [44], this torque corresponds to a preloading force of 41 kN. Two Photron Fastcam SA5 high-speed cameras (Photron) are arranged stereoscopically. Each is positioned 1100 mm from the aluminum plate's center. Images are recorded at 20,000 frames per second. Recording begins when an electric circuit is intentionally disrupted during detonation. The selected shutter time is 25 microseconds. Anticipating significant out-of-plane displacements (OPDs), the camera apertures are reduced to increase the depth of field. To compensate for the reduced aperture, the area of interest is illuminated using three high-intensity LED lights (Correlated Solutions, Homo, SC, USA). The captured images have a resolution of 512 \(\times\) 512 pixels to cover the 400 \(\times\) 400 mm\({}^{2}\) plate surface, resulting in a pixel size of 0.78 mm/pixel. A subset size of 21 \(\times\) 21 pixels with a subset spacing of 3 pixels and a strain filter of 15 is used for the digital image correlation (DIC) process using VIC 3D 2007 software. Figure 1: (**a**) Overview of the set-up showing the steel frame, two high-speed cameras (Photron Fastcam SA5, Photron, Bucks, UK) arranged stereoscopically, and three LED spots; (**b**) speckle pattern applied on the aluminum backplate (EN AW-1050 A H24, Thyssenkrupp, Brussels, Belgium) enabling measuring the displacement and in-plane strain fields; and (**c**) 20 g of C4 explosive charge in a spherical shape and electric detonator. The response of the bare aluminum plate to that of the plate protected with three distinct configurations of mineral foam, as shown in Figure 3, are compared to evaluate the effectiveness of the SC. The difference between the three foam configurations lies in the free space available for the foam to expand compared to the total volume of the foam. Therefore, the ratio \(\zeta\), denoting the ratio between the lateral surface for the foam to expand and the total volume of the foam is introduced. \[\zeta=\frac{\text{Lateral surface }[\text{mm}^{2}]}{\text{Total volume }[\text{mm}^{3}]}, \tag{1}\]  
The values of \(\zeta\) are increased progressively from configuration A to configuration C. Three tests are performed per configuration to evaluate the repeatability of the measurements. The loading is generated by detonating 20 g of C4 (25 g TNT equivalent) positioned 250 mm from the tested plates' center. The selection of explosive mass and standoff distance is intended to induce significant inelastic deformation of the aluminum plate. The detonation is initiated using an electric detonator containing 1 g of PETN. Figure 1c provides a detailed view of the explosive charge, detonator and their respective positions. The foam samples are extracted from panels with a 60 mm thickness, resulting in a standoff distance of 188 mm (considering the 2 mm thick front skin made of aluminum, as illustrated in Figure 2). A double-sided self-adhesive tape is used to secure the mineral foam. This tape is applied to both the aluminum backplate and the front skin. Attaching the foam in this manner ensures a secure bond between the foam and the aluminum components while avoiding any increase in the overall structural strength. To prepare for testing the 2 mm thick aluminum plates under blast conditions, preliminary experiments were conducted using a 15 mm thick aluminum plate.