52.4 Result 52.4.1 iSALE and CTH VISAR Results Figure 52.4 presents a comparison of iSALE 2-D simulated results versus Georgia Tech experimental VISAR results. As expected for a smaller density than the experiment’s density, the arrival time of the shock waves for each experiment compared to the experimental results is greater and therefore manifests a softer response. While the experiment’s densities were on average of 1.70 g/cm3 (65 % dense), iSALE’s density was 1.63 g/cm3 (61 % dense). The peak particle velocity values of the iSALE results would not match due to this lower density change, and this is presented in Fig. 52.4 where the iSALE simulations under predicted the particle velocities at the interface. The flyer impact velocity increases from right to left of the plot and the dotted black line represents the simulated results. Averages of these iSALE peaks were taken and then by theoretical Shock, Particle Velocity impedance matching, the resulting particle velocities in Table 52.3 were calculated and utilized to create a hugoniot. The impedance matching method assumed conservation of mass, momentum, and energy, as well as Rankine-Hugoniot jump conditions. In Fig. 52.5, there are three comparisons of CTH 3-D simulated VISAR readings. Figure 52.5a, b show the simulated results versus the experimental results, one without stiction and the other with stiction, respectively. Figure 52.5c shows the comparison of the simulations with the different particle interactions. Figure 52.5a shows a much softer response than Fig. 52.5b, since the particles are acting more like a homogenous material than a granular material. This is noticed by the stiffer, faster shock wave arrival as well as a shorter rise time in the plots. In addition, the heterogeneity of the granular material is recognized by the fluctuations in Fig. 52.5a compared to Fig. 52.5b since there are more interactions among the sliding particles compared to the welded particles. There is a wide range of variation in the plateaus of the particle velocities of both types of simulated results (Fig. 52.5c), with the simulations with stiction possessing higher particle velocities than the simulations without stiction. As will be seen in Fig. 52.6 of the Hugoniot results, the simulated results with sliding manifests a much more accurate result in comparison to the experiments than the over predicted and stiffer response of the stiction model. Table 52.3 lists all of the results from the experiment as well as the simulations. Particle velocity (Up) was calculated by taking the plateaus of the VISAR readings in Figs. 52.4 and 52.5 and using theoretical impedance matching to find the particle velocity at the copper driver, sand interface. Shock velocity (Us) was calculated by using the following equation: Table 52.3 Initial densities and results Impact velocities are 413, 618, 754, and 998 m/s Initial density, ρ (g/cm3) Particle velocity, Up (m/s) Shock velocity, Us (m/s) Experimental results 1.76 382 1,620 Us ¼1.78Up + 924 1.71 570 1,939 1.72 678 2,100 1.73 899 2,547 iSALE 2D 1.63 398 1,267 Us ¼1.93Up + 529 1.63 588 1,690 1.63 701 1,923 1.63 928 2,293 CTH 3D without stiction 1.76 397 1,817 Us ¼1.41Up + 1201 1.71 583 1,948 1.72 692 2,169 1.73 917 2,532 CTH 3D with stiction 1.76 378 2,462 Us ¼0.28Up + 2285 1.71 558 2,381 1.72 672 2,397 1.73 888 2,598 52 Mesoscale Simulations of Dry Sand 383
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