Results and modifications

Figure 8.3: Maximum damage on plate (front and back).

Figure 8.3 illustrates the maximum damage for the initial model, and it is clear that the con-crete plate did not experience as much damage as seen in the experiment. However, damage resembling the bending failure pattern was visible at the back of the plate. The front also managed to recreate some of the physical behaviour. In order to approach the behaviour of the physical experiments, it was necessary to reduce the capacity of the material. To do this, it was first decided to reduce the damage threshold for both the brittle and the ductile damage.

Figure 8.4 shows the damaged plate with a brittle and ductile damage threshold of 0.5 and 0.25 at the time of the maximum applied load. Erosion of elements in a bending failure pattern could be seen in the model with damage thresholds of 0.25 (see Figure 8.4b). How-ever, the model would still not generate sufficient damage and the FSI effects were minimal, if present at all. Further modifications of the model was therefore required.

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(a) ENDT & ENDC = 0.5 (b) ENDT & ENDC = 0.25

Figure 8.4: Front and back of damaged plate.

In the initial model, associated plastic flow was employed since it was the default in the DPDC model [20]. Non-associated plastic flow was employed in a new version of the FSI model by introducing the parameter COPP. COPP is defined as a coefficient for the plastic potential, and an advised value of 0.2 was used [20]. It was expected that this would lead to a reduced capacity. Figure 8.5 shows the behaviour of the plate with the introduction of COPP = 0.2 and a damage threshold of 0.5. Note that only half of the fluid mesh is visualised to enable a clear view of the plate. The Europlexus file for the visualisation is found in Appendix D.3.

As seen in Figure 8.5, the plate detached itself from the end of the driven and was pushed in the opposite direction from what occurred in the experiment. To avoid this in further simu-lations, the boundary of the dump tank was assigned an absorbing material. The reflection of the pressure wave in the dump tank was thus assumed to exert no significant influence.

CHAPTER 8. NUMERICAL STUDIES

(a) t = 0 ms (b) t = 35 ms

(c) t = 68 ms (d) t = 100 ms

Figure 8.5: Model with non-physical behaviour.

Further, the approach was to change the damage threshold to get a total collapse of the plate.

Figure 8.6 shows the plate at the time of maximum load (left) and at the end of the loading (right). As seen in the figure, a damage threshold of neither 0.9 nor 0.5 gave a total collapse.

It did however result in a lot of damage in the plate as many elements were eroded.

For a damage threshold of 0.25, total collapse occurred, and selected frames from the simu-lations can be seen in Figure 8.7. Figure 8.7a shows the plate as the shock wave first impacts the plate, while the point of maximum load can be seen in Figure 8.7b. For collapse to occur even earlier, the damage threshold was reduced to 0.2, where Figure 8.8 illustrates the cor-responding damage process. The Europlexus file for the final visualized simulation is found in Appendix D.2.

CHAPTER 8. NUMERICAL STUDIES

(a) ENDT & ENDC = 0.9 (b) ENDT & ENDC = 0.5 Figure 8.6: Back of plate at maximum load (left) and end of loading (right).

(a) t = 21 ms (b) t = 35 ms (c) t = 37 ms

Figure 8.7: Collapse of plate with ENDT & ENDC = 0.25.

(a) t = 21 ms (b) t = 32 ms (c) t = 34 ms

Figure 8.8: Collapse of plate with ENDT & ENDC = 0.20.

The primary reason for conducting the FSI analysis was to retrieve the pressure on the

CHAPTER 8. NUMERICAL STUDIES collapsing plate. It was interesting to see the difference from a pure Eulerian simulation and the resulting FSI effects in a fully coupled simulation. It was however discovered that the FSI analysis did not obtain the same magnitude of pressure on the plate as the Euler analysis, even when the plate was completely rigid. The FSI effects was therefore at first thought to be larger than they really were. Figure 8.9a illustrates the difference of the pressure for a pure Eulerian analysis and an FSI analysis with a completely rigid plate. The pressure was taken from the position of sensor 409. In theory, this pressure is supposed to be equal, and the deviation is most likely due to the the adaptivity algorithm. In fact, the current version of Europlexus uses the arithmetic average when plotting the pressure in an automatically refined element with descendants. This means that the current code will take the arithmetic average of all its active descendant elements and not a weighted average, which would be more accurate. It should be noted that this is currently being revised in Europlexus, and the weighted average will be used in the next version of the code [66].

(a) Deviation in the reflected pressure (b) Illustration of the FSI effects

Figure 8.9: Pressure in the location of sensor 409.

In order to detect possible FSI effects, the pressures from the FSI analyses were compared to the one with a rigid plate. Figure 8.9b shows the pressures in the location corresponding to sensor 409 for the models with damage thresholds of 0.50, 0.25 and 0.20. As seen in Figure

CHAPTER 8. NUMERICAL STUDIES

8.9b, it is evident that FSI effects were present in the the simulations with damage thresh-olds of 0.25 and 0.20. The peak pressure occurs both earlier and with a lower value than for the analysis with the rigid plate. Only small FSI effects were detected in the analysis with damage thresholds of 0.50.

Of the performed analyses, the one with the smallest damage threshold gave a response closest to the physical experiment. Figure 8.10 shows the pressure in sensor 409 in the exper-iment compared with the simulation. Note that the storage interval of the pressure was not frequent enough to capture the discontinuities in the experiment. In the physical experiment, a pressure fall from about 18.5 bar, followed by a plateau, was visible in the pressure history in sensor 409. This pressure fall probably occurred due to leakage of the pressure through cracks in the plate. The numerical model was not able to capture this pressure fall, primarily due to the coarse mesh of the plate. In order to describe crack propagation in a structure, a much more refined mesh is required. However, a refinement of the mesh was not investigated due to a massive increase of computational costs. The conducted analyses presented in this section took about 7 hours each. It should be noted that a damage driven adaptivity is currently being developed in Europlexus, which would be an interesting investigation in the future.

Figure 8.10: Experiment vs FSI analysis.

CHAPTER 8. NUMERICAL STUDIES In order to retrieve a good approximation to the pressure on the plate from the experiment, a much more comprehensive FSI analysis proved to be necessary. In addition to a finer mesh, a more accurate modelling of the boundary conditions of the plate would be required.

As the FSI analyses did not provide a satisfactory approximation to the pressure, it was necessary to find the load on the plate in a different way. The load was needed for the nu-merical study in IMPETUS, where the different experiments would be attempted recreated.

It was selected to use an altered version of the pressure in sensor 409 (see Figure 8.11). This seemed reasonable as the pressure in the sensor and plate did not differ much in the cali-bration tests. Unfortunately, to check whether this was true for the FSI analysis turned out to be difficult, and the pressure on the plate was not retrieved. It should be noted that the pressure on the collapsed plate would not be uniform and that using the same pressure over the entire plate would be a simplification.

Figure 8.11: Assumed pressure on collapsed plate.

CHAPTER 8. NUMERICAL STUDIES