## 4 Numerical Work
### Shock Tube Tests
#### 4.3.2 Blast Simulation Results
For XPS-700, this localisation effect is almost non-existent since the plateau stress of XPS-700 is high compared to the applied load. Figure 21: Distribution of internal energy in numerical simulations of tests with 10 bar firing pressure. Figure 22: Deformation profiles and plastic strain fields from numerical simulations of test Sw_250_P10. When the viscoplastic formulation for the core materials is applied, the back-skin midpoint displacement is reduced in all simulations since the viscous increase in plateau stress increases, as expected, the stiffness of the sandwich panels. The introduction of viscoplasticity also reduces the effect  
Figure 23: Deformation profiles and plastic strain fields from numerical simulations of test Sw_400_P10. Figure 24: Deformation profiles and plastic strain fields from numerical simulations of test Sw_700_P10. of modelling the density distribution, as the viscous increase in plateau stress will act to normalise the difference introduced by the density variation. This is especially noticeable in the core compression for XPS-400 and XPS-700, where there is almost no difference between the CD-VP and DD-VP model, as seen in Figure 20. This strong influence of the viscoplastic formulation on the numerical results indicates that the plastic strain rates in the problem are high (about 500 s\({}^{-1}\) in the core material for XPS-250 at P15) so that a viscoplastic formulation of the core material is recommended to describe an accurate response. Trends in midpoint displacement at a driver pressure of 12 bar are shown in Figure 14. The response is similar to that observed at 10 bar pressure, but with a smaller difference in displacement between the CD and the DD model and a smaller reduction in displacement when viscoplasticity is included. The midpoint core compression for XPS-250, Figure 15, does not increase by the same relative magnitude between CD and DD as for the lowest load because the higher load activates more of the constant density material. For XPS-400, the relative increase in midpoint core compression is higher between CD and DD than at the lower load level, which indicates that at this load level more of the core material has a low enough plateau stress to initiate plastic deformations with the DD model. For XPS-700, the midpoint core compression is very similar to the lower load level, as the plateau stress is still too high to allow significant plastic deformations regardless of how the material is modelled. The distribution of internal energy from the simulations at this load level, Figure 16, follows the trends seen at the lowest load level. Here, the highest dissipation is seen for the XPS-250 material with DD, while XPS-400 with the viscoplastic formulations shows a clear reduction in internal energy. XPS-700 yields almost the same result for all material formulations. An interesting observation is the reduced internal energy for the back skin and the increase in internal energy for the front skin for both XPS-250 and XPS-400 when the formulation is changed from CD to DD. When the distributed density model is applied, the reduced plateau stress in the low-density centre causes plastic deformation to occur at a lower transmitted pressure, and the pressure load transferred through the core to the back skin is thus reduced. Deformation profiles for XPS-250 and XPS-400, shown in Figures 17 and 18, exhibit the same trends as at the lower load level, where more plastic deformation occurs in the lower-density centre of the core for both materials. Furthermore, the inclusion of a viscoplastic formulation reduces the plastic deformations in both models. The deformation profiles for XPS-700 are not displayed for brevity, as this material did not show any significant plastic deformations at this load level. Midpoint displacements for the highest load level, i.e., 15 bar, are presented in Figure 19. At this load level, XPS-400 has a higher midpoint displacement than XPS-250 with the CD model.