# Double-Bend and Semi-Spherical Energy Deflectors' Blast Load Efficiency--A Comparative Study
## 3 Numerical Modelling  
In order to reproduce the experimental test conditions, a numerical model of the entire test stand was prepared. The prepared model allowed for easy change of the tested energy-dissipating structures, so it was possible to test the effectiveness of various geometries. The results of the experimental tests were used to carry out the validation process of the created numerical model.  
Many methods allow a numerical analysis of the process of detonation of explosive charges. One of the most popular and most straightforward to implement is the ConWep  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rupture** & **Yield** & **Ultimate** & **Strain at** & **Young’s** & **Poisson’s** \\
**[MPa]** & **Strength** & **Strength** & **Failure** & **Modulus** & **Ratio** \\
**[MPa]** & **[MPa]** & **[MPa]** & **[-]** & **[GPa]** & **[-]** \\ \hline
536.7 & 353.3 & 623.2 & 0.308 & 209.6 & 0.307 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of quasi-static test results for 41 Cr4 material.  
Figure 5: Specimens used for material testing.  
Figure 6: Engineering stress–strain curve of 41 Cr4 steel obtained from quasi-static tensile testing.  
method, based on empirical equations obtained from conducting a series of experimental tests [36; 37]. This method makes it possible to perform approximate analyses when it is essential to ensure a short analysis time for spherical charges placed in the air or semi-spherical charges placed on the ground. However, its use is associated with some disadvantages (in addition to the only two explosive charge shapes mentioned earlier), one of the most important of which is the inability to simulate the propagation of the wave reflected from the target [36]. It is a significant drawback of using such an approach that when the wave interaction target has a more complicated shape, there is an introduction of significant errors in the results. For this reason, the authors of the presented study decided to use the ALE (Arbitrary Lagrangian Eulerian) approach.  
The ALE method combines both commonly used approaches of the finite element method, i.e., the Lagrangian and Eulerian approaches. In the Lagrange formulation, the material is closely related to the finite element mesh describing it, i.e., as the object deforms, the mesh deforms. This approach is used mainly in simulating solids. For liquids, it is more advantageous to use the Euler formulation, wherein the finite element mesh is fixed and does not change its position with respect to the object. This approach avoids many problems arising during large deformations of the mesh. The disadvantage of this solution is the need to discretize the additional space surrounding the object under study. The idea of the ALE approach is to exploit the advantages of both formulations [38]. With the use of FSI (fluid-structure interaction) when modelling the detonation phenomenon, the individual elements of the solid are described using the Lagrange formulation. In contrast, the detonation products and the air surrounding the system are described using the Euler formulation.