# Numerical Identification of Material Model Parameters of UHPFRC Slab under Blast Loading
## 5 Computational Model  
The aim of this phase was to create a computational model and carry out a numerical simulation that in essence imitates experiment no. 6 (Table 4), i.e., the blast loading of the concrete slab by the charge of 225 g TNT at 200 mm from the test specimen of dimension 500 mm \(\times\) 500 mm \(\times\) 60 mm made from UHPFRC. From the geometric model of the concrete slab, finite element mesh was created. For the discretization of the model, Lagrangian solid elements (eight node hexahedron solid elements with one integration point) of the 10 mm edge length with an aspect ratio of unity were used with the Winfrith constitutive material model assigned (Figure 5). The 2% fibre reinforcement volume ratio in the concrete was modelled using the smeared reinforcement method implemented into the used Winfrith concrete material model. The idealized discretized model of the test bed was created from 10 mm shell elements (Belytschko-Tsayone point integration shell element) without degrees of freedom with rigid material model assigned. To simplify the boundary conditions, it was assumed that the friction between the surfaces of the test plate is so great that it does not allow the plate to move in the horizontal direction during the pressure wave load, nor its rotation. To simulate the explosion itself, the approach of explicit modelling of air and explosive was used using Multi Material ALE (Arbitrary Lagrange Eulerian, one integration point element) formulation of hexahedron 10 mm edge length elements, with an aspect ratio of unity with a second order advection scheme for material transport. This element formulation allows air and explosive materials to share the same elements as the air-filled domain to provide space into which explosive materials of higher density may be transported as the simulation progress. This formulation allows materials to flow through the ALE mesh, while material boundaries or interfaces do not coincide with the mesh lines and the material interfaces are internally reconstructed at each time step based on the volume fractions of the materials within the elements [56]. In the initialization phase, the entire ALE computational domain was filled with air. Air was defined with the null material model that allows linear polynomial equation of state (EOS) to be used without computing deviatoric stress. Setting the gamma law EOS and material model parameters according to Table 6 approximates air as an ideal gas at 0.101 MPa pressure [60]. More about this model, equations and used parameter values can be found in [61; 62]. Where C4 and C5 are constants of linear polynomial EOS, E0 is initial internal energy per unit reference volume, V0 is initial relative volume and \(\rho\) is the density of the air. After the calculation has started, defined ALE volume fraction was filled with the explosive. TNT explosive was defined with High Explosive Burn Material with the Jones-Wilkins-Lee equation of state (JWL EOS), where JWL EOS is describing relationships between relative volume, internal energy per volume and blast pressure of detonation products. Chemical energy released during the time interval is stored in these burnt products of the explosive and are assumed to behave as a homogeneous gas undergoing adiabatic thermodynamic process defined by JWL EOS. The High Explosive Burn Material model controls an explosive's detonation behaviour. In this material type, burn fractions direct a chemical energy release during detonation, and explosive pressure in an element \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Linear Polynomial EOS**} & \multicolumn{2}{c}{**Null Material**} \\
**C4 (-)** & **C5 (-)** & **E0 (J/m3)** & **V0 (-)** & \(\rho\) (kg/m3) \\ \hline
0.4 & 0.4 & 253.4 \(\times\) 103 & 1 & 1.225 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameters of linear polynomial EOS and null material model for air. Figure 5: Modelling of the blast load of the concrete slab-displacement (mm) plot of the specimen in 3 ms time instant.