## 4 Numerical Work
### Shock Tube Tests
#### 4.3.2 Blast Simulation Results  
One emphasis in the numerical part of this study is to examine the influence of varying the material description of the core material. Numerical and experimental results are compared, but it was not expected that the rather simple numerical model could exactly replicate the experimental results. This is partly because the blast load is included without accounting for FSI effects, and thus not ideal for an accurate prediction of the structural response. However, it is expected that the trends in the response are correctly predicted even though FSI effects are not considered. Simulation results for load level P12 and P15 have been moved to Appendix A.2 to reduce the data amount presented in the text. Midpoint displacements from numerical simulations of the aluminium skins only (i.e., without cores) are compared with the experimental results in Figure 17. As the load applied numerically does not account for FSI effects, the numerical displacements are consistently larger than the experimental values. These results agree with the observations of [PERSON] et al. [26] for single steel plates subjected to a similar blast load. Overall, the results from the simulations show that the applied numerical model predicts the structural response reasonably well. In these simulations, no fracture criterion was applied. However, the value of the Cockcroft-Latham fracture parameter \(W\)[44] is calculated during simulations when MAT_107 is used. The value of \(W\) from these simulations was compared to the value obtained in simulations of the tensile tests until fracture appeared in the physical test. Based on this comparison, it is expected that fracture would have occurred in the 15 bar simulation and not in the 12 bar simulation. This is consistent with the experimental results. The numerical results from the simulations of sandwich components will be presented in two parts. First, the numerical results obtained with the original, constant-density Deshpande-Fleck crushable foam model are compared to the experimental data to reveal the predictability of the standard model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test**} & **Nominal Firing** & \(P_{r,max}\) & \(t_{d+}\) & \(b\) \\  & **Pressure [bar]** & **[kPa]** & **[ms]** & **[–]** \\ \hline P10 & 10 & 446.2 & 35.4 & 1.571 \\ \hline P12 & 12 & 519.3 & 39.8 & 1.892 \\ \hline P15 & 15 & 606.6 & 44.1 & 2.025 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters of the Friedlander equation curve-fitted to the pressure measurements from massive plates tests. Figure 17: Comparison between experimental and numerical mid-point displacements for aluminium skins only. Second, the difference in numerical results when incorporating distributed density and viscoplasticity to the material model is compared to the original, constant-density Deshpande-Fleck model. Numerical midpoint displacements from simulations of the tests with the original Deshpande-Fleck model at 10, 12 and 15 bar firing pressure are presented in the leftmost graphs in Figures 18, A5 and A10, respectively. At 10 bar firing pressure, Figure 18 shows that the midpoint displacement from the simulation with XPS-250 is very close to the experimental result, while the numerical midpoint displacements for XPS-400 and XPS-700 are significantly higher than the experimental values. The difference between XPS-400 and XPS-700 is within the same range numerically as experimentally. The excellent agreement between experiments and simulations for XPS-250 is somewhat unexpected, since the method used to apply the loading should provide conservative results, i.e., a higher numerical than experimental displacement. Also, the difference in displacement between XPS-250 and XPS-400 is expected to be larger. The reason for this result is not entirely apparent, but as shown in Figures 22-24, the simulations with the weakest core material have significantly higher plastic deformations of the core compared to the other two core materials.