Input files
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CollidingPlates.KIN, CollidingPlatesVoid.KIN,COPP3333.KBT
Download CollidingPlates.zip
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Description
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In this one-dimensional KB1 calculation, a shock is initiated when two copper plates moving at high velocity collide. The example demonstrates the use equation-of-state data from the KB tables and the application of KBView to predict the shock properties. In the first calculation, plates moving a velocities +-5.13 km/s touch at the moment of impact. The left-hand region extends from x = -1.00 cm to 0.00 cm and the right-hand region from x = 0.00 cm to 1.00 cm. The material table for both regions is COPP3333.KBT. Both regions are initially at normal temperature and density. The simulation covers 1.0 us with spatial data records at intervals of 0.1 us. Probes at the system boundaries measure the width and other properties of the assembly as a function of time.
A second calculation (CollidingPlatesVoid) was performed to illustrate use of the KB1 VOID model. The plates had an initial separation of 0.2 cm, so the predicted time to collision was 0.195 us. The void model used DV = 0.01 cm and PV = 600.0 GPa.
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Results
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With the material COPP3333.KBT loaded, KBView was used to generate Hugoniot curves of the form P(Up) and Us(Up). Here, Up is the speed of particles in the undisturbed medium, P is the shock pressure and Us is the speed of the shock relative to the medium. The program creates plots (top figures) and the following text information:
Hugoniot curve P(Up) for material: COPP3333.KBT
Initial density (gm/cm3): 8.9300E+00
Initial temperature (deg-K): 2.9800E+02
Up(km/s) P(GPa) Us(km/s)
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5.0741E-01 2.1562E+01 4.7421E+00
1.0444E+00 5.1840E+01 5.5502E+00
1.9722E+00 1.2169E+02 6.9055E+00
2.3206E+00 1.5367E+02 7.4121E+00
3.1739E+00 2.4848E+02 8.7643E+00
4.1030E+00 3.7158E+02 1.0139E+01
5.1281E+00 5.3153E+02 1.1605E+01
7.3459E+00 9.5641E+02 1.4578E+01
9.8616E+00 1.5691E+03 1.7817E+01
1.2641E+01 2.4020E+03 2.1278E+01
1.7622E+01 4.3143E+03 2.7415E+01
2.1707E+01 6.2875E+03 3.2435E+01
2.6522E+01 9.0768E+03 3.8323E+01
3.4078E+01 1.4456E+04 4.7502E+01
3.8974E+01 1.8597E+04 5.3433E+01
7.8434E+01 7.0725E+04 1.0098E+02
The number of points is determined by the number of values in the KB tables. For a particle speed Up = 5.13 km/s, the predicted shock pressure is 5.32 GPa and the shock velocity is 11.61 km/s. The lower figure shows KB1 results plotted by KB1V. The plot shows pressure as a function of position at times 0.4 us and 0.8 us. The pressure is 532 GPa, in agreement with the prediction from the Hugoniot curve. The shock velocity in the rest frame, determined by comparing the change in the front position between the two curves, is 6.50 km/s. To determine the shock velocity relative to the undisturbed medium, we must add the particle velocity, Us = 6.50 km/s + 5.13 km/s = 11.63 km/s. The probe signals on the outher boundary show that the plate width shrinks from 1.00 cm to a minimum of 0.56 cm at 0.87 us.
The magnitude and velocity of the shock wave in the calculation with an initial void were identical to the previous calculation. Inspection of the envelope turning time with Probe showed a delay 0.185 us.
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Comments
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The KB manual discusses the theory of shock waves and the significance of the Hugoniot curve.
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