## 2 Numerical Simulation of Experimental Measurements
### Computational Model  
As mentioned above, the simulation was performed in LS-Dyna, which was developed as an explicit numerical analysis code and has since been widely used to solve high strain-rate problems or dynamic and impulsive problems with its advanced Eulerian, Lagrangian and Arbitrary Lagrangian-Eulerian (ALE) solvers [8]. The setup of the simulations follows the steps and recommendations from [8; 9; 10; 11; 12; 13; 14], while using values of input parameters from previous works of the authors [5]. From the CAD model of the slab with dimensions of 700 \(\times\) 700 \(\times\) 60 mm, a mesh of finite elements was generated. The _Solid_ type hexahedron elements with an edge length of 2.5 mm were used to discretize the model (Figure 1), [10]. The idealized discretized model of the supporting frame was created from the _Shell_ type elements of _Rigid_ material with a size of 2.5 mm without degrees of freedom (Figure 1), [10]. To simplify the boundary conditions, it was assumed that the friction between the surfaces of the test slab and the supporting frame did not allow the slab to move or rotate horizontally during the pressure wave load. _Mat_Wintfith_Concrete_ was chosen as the material model of the concrete. This nonlinear material model is intended for modeling plain and reinforced concrete [11; 12; 13]. The influence of the deformation rate on the mechanical-physical properties of concrete is covered in the _Mat_Wintfith_Concrete_ material model via dynamic coefficients of material parameters, which change the basic material parameters of concrete acquired from quasi-static tests. As described in [12], this option can be activated on the material model card by setting \(rate=0.0\) (Table 1). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**MAT\_WINFRITH\_CONCRETE**} \\ \hline mid & ro & tm & pr & usc & uts & fe & asize \\ \(1\) & \(2.37\times 10^{-6}\) & 40 & 0.2 & 0.069 & 0.0059 & 0.0005 & 5 \\ \hline e & ys & eh & uelong & rate & comm & conl & cont \\ \(0.00\) & \(0.00\) & \(0.00\) & \(0.00\) & \(-5\) & \(0.0\) & \(0.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material model card used in LS-Dyna for Winfrith Concrete for batch A2 (kg, mm, ms, kN, GPa). Figure 1: CAD models: (**a**) The mesh of the concrete slab: \(700\times 700\times 6\) mm; (**b**) The supporting frame: outer dimensions \(700\times 700\) mm, inner dimensions \(400\times 400\) mm. Figure 2: Explicitly modelled beam reinforcement of MAT_PLSTIC_KINEMATIC, constrained in \(700\times 700\times 60\) mm concrete mesh. When modeling the reinforcement of the slabs of batches A2, explicit modeling of the fiber reinforcement (Table 2, Figure 2) was used. Interaction of the reinforcement with concrete mesh was controlled by the _Constrain_Beam_In_Solid_ card. Figure 4: Reverse side of a damaged slab from the batch A2: (**a**) Cracks; (**b**) Cracks and crack opening strain color contours. Figure 3: The ALE mesh of the dimensions \(850\times 850\times 1400\) mm: (**a**) Filled with air (green) encapsulating the meshed slab (red); (**b**) Filled with explosive material (blue) in the 600 mm distance from the slab (black). Table 1 describes the _Winfrith_ material model of concrete with cubic compressive strength \(ucs\) = 69.7 MPa, tensile strength \(uts\) = 5.9 MPa, density \(ro\) = 2365 kg\(\cdot\)m\({}^{-3}\), maximum aggregate size \(asize\) = 5 mm, fracture energy \(fe\) = 500 J\(\cdot\)m\({}^{-2}\) with strain rate effects turned on (\(rate\) = 0.0). Table 2 describes the material properties of the steel fiber reinforcement, where density \(ro\) = 7860 kg\(\cdot\)m\({}^{-3}\), [PERSON]'s modulus \(e\) = 203 GPa, [PERSON]'s ratio \(pr\) = 0.3, yield stress \(sigy\) = 950 MPa and tangent modulus \(etan\) = 3 GPa. The fibers were generated according to specification of the batch A_2. An idealized model of the reinforcement as 60 mm long steel fibers of the quantity of 60 kg\(\cdot\)m\({}^{-3}\) of the concrete mix was generated.