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LA-UR- ;D-{)/5¥3 Approved for public release; distribution is unlimited. NATIONAL LABORATORY --- EST . 1943 --- Title: Mesoscale Modeling of Metal-loaded High Explosives Author(s): John B. Bdzil, DE-9 & Dept. Mech. Sci. Eng., University of Illinois @ Urbana-Champaign Brandon Lieberthal, Dept. Mech. Sci. Eng., University of Illinois @ Urbana-Champaign D. Scott Stewart, Dept. Mech. Sci. Eng., University of Illinois @ Urbana-Champaign Intended for: 14th International Detonation Symposium April 11-16, 2010 Coeur d'Alene Resort, ID Los Alamos National Laboratory, an affirmative action/equal opportunrty employer, is operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE·AC52·06NA25396. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness. Form 836 (7/06)
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  • LA-UR- ;D-{)/53 Approved for public release; distribution is unlimited.

    ~Alamos NATIONAL LABORATORY --- EST . 1943 ---

    Title: Mesoscale Modeling of Metal-loaded High Explosives

    Author(s): John B. Bdzil, DE-9 & Dept. Mech. Sci. Eng., University of Illinois @ Urbana-Champaign Brandon Lieberthal, Dept. Mech. Sci. Eng., University of Illinois @ Urbana-Champaign D. Scott Stewart, Dept. Mech. Sci. Eng., University of Illinois @ Urbana-Champaign

    Intended for: 14th International Detonation Symposium April 11-16, 2010 Coeur d'Alene Resort, ID

    Los Alamos National Laboratory, an affirmat ive action/equal opportunrty employer, is operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DEAC5206NA25396. By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution , or to allow others to do so, for U.S. Government purposes. Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publ ication or guarantee its technical correctness.

    Form 836 (7/06)

  • Mesoscale Modeling of Metal-loaded High Explosives

    John B. Bdzil', Brandon Liebertha]", D. Scott Stewart Department of Mechanical Science and Engineering

    University of Illinois, Urbana, IL, 61802

    Abstract. We describe a 3D approach to modeling multi-phase blast explosive, which is primarily condensed explosive by volume with inert embedded particles. These embedded particles are uniform in size and placed on the array of a regular lattice. The asymptotic theory of detonation shock dynamics governs the detonation shock propagation in the explosive. Mesoscale hydrodynamic simulations are used to show how the particles are compressed, deformed, and accelerated by the high-speed detonation products flow.

    Introduction

    Metal-loaded blast explosives (MBX) and metalized enhanced-blast explosives (EBX) are of interest because with the addition of small metal particles to a high-performance explosive (HE), such as HMX, RDX or TNT, one can tailor the profile of "applied pressure"-vs-time (and the total delivered impulse). Although the explosives applied pressure is lowered, it is sustained for a longer time. These metal particles are accelerated and heated by the primary products of detonation. This increases the energy transfer from the explosive to a target, and thus enhances target damage. When these metal particles are reactive, such as with aluminum particles, a further enhanced-blast performance can be obtained (depending on particle size/explosive size) as the particles either react with the hot detonation products or burn in air as the particles are ejected from the explosives fireball (thermo-baric explosive) [1,2].

    We describe our mesoscale modeling of the interaction of the detonation wave in a HE contain ing embedded inert partic les [3, 4]. We restrict our attention to situations where: I) the

    diameter of the metal particles, d, is either comparable to or larger than the explosives detonation reaction-zone length, h, (dlh I), 2) the shock speed in the metal particles is less than the detonation speed, and either 3) the particles are inert or 4) the particles react with the hot detonation product gases on a time scale longer than the explosives reaction time scale. In this dlh / limit and with the above assumptions, detonation shock dynamics (DSD) provides an adequate representation of how the detonation wave in the explosive successfully propagates via circuitous path in the explosive between the particles (see Figure I).

  • Fig. I. A cartoon that depicts how a detonation wave propagates in a metal-loaded HE. Particles

    significantly affect the mean detonation propagation speed .

    1:/ :(,. e . Fig. 2. A density color palette plot showing an instantaneous (t = 6 .25 J.ls) projection of the density in the plane, y = 0.5, passing through the center ofa SC array of 5 steel spheres embedded in both the products of detonation and in fresh ABS explosive [7]. The Cartesian z-axis is horizontal, the x-axis is vertical, and the y-axis points out of the plane of the paper. The lines are the current boundaries of the explosive cel,ls that were originally lxlxl-unit cubes. The original sphere radius is r = 0.363; corresponding to an initial volume fraction of inert of 0.20. The detonation is moving to the right.

    We begin by describing the DSD method, the scaling laws for our problem and introduce the metal-loaded HE unit cell problem. We construct our explosive from a collection of these 3D unit cells, and restrict attention to loadings of 20% by volume particles in these particle-loaded explosives. Specifically, here we consider a mono-modal particle distribution with the following symmetries: simple cubic array (SCA), body-centered cubic (BCC) and face-centered cubic (FCC). Under the constraint of 20% by volume particles, these changes in unit cell geometry bring with them changes in the particle diameter relative to the explosives intrinsic reaction-zone length. By stacking these unit cells, we are able to study detonation propagation in semi-infinite beds of these metal-loaded explosives. By then averaging the results from DSD front propagation calculations, we develop effective DSD propagation laws for these composite explosives [5] .

    The embedded particles are compressed and accelerated by the: I) the oblique shock drive provided by the passing detonation wave and 2) the drag forces associated with the streaming of the detonation products past the particles . Because the detonation wave speed in the explosive and the shock speed in the particulate material are in general disparate, shock focusing and/or diffraction occurs in the loaded particles. This can generate both regions of high pressures and tensions in the particles. Due to the

    heterogeneity in the pressure loading of the particles, the particles are deformed; this ultimately can lead to the fragmentation of the particles under some loading scenarios. Experiments performed on the shock-and-release loading of a copper sphere embedded in a matrix of I gm/cc polystyrene shows large deformation and fragmentation of the copper sphere [6]. Here we present results from our medium-resolution, three-d imens ional hydrodynamic simu lations of detonation in a highlly symmetric array of 10 spherical particles packed in a SCA and aligned along the z-axis. We consider the shock-compression, acceleration and deformation of the particles by a constant speed, programmed-burn detonation wave moving in the z-direction. These detai led mesoscale simulations show that the dynamic loading of the particles is divided into two regimes: I) a non-isentropic, shock-loading phase, which ends with the particle and explosive products pressures being nearly equilibrated, that is then followed by 2) a nearly isentropic phase. where "form drag" causes the particles to be further accelerated by the speedier flow of the detonation products. A plot of density along a symmetry plane, a plane passing through the centers of 5 steel sphere embedded in the SCA unit cells of explosive, is shown at 13.5 f.ts in Figure 2. The explosive is modeled using our ABS explosive model [7]. We describe both the loading of low-impedance plastic spheres and high-impedance metal spheres.

    DSD Detonation Propagation Methodology

  • The DSD-limit applies when an explosives detonation reaction zone is broadly curved in the transverse direction when measured on the scale of the reaction zone in the normal direction . Then the normal speed of the detonation front , D'I) is a function of the radius of curvature of the detonation front's shock, K [8].

    DSD front

    Fig. 3. The boundary condition applied on W at all edges of the explosive depends on whether W < Ws or W > w,' where Ws is the value of the angle corresponding to a son ic flow at the edge of the explosive. When W < ws , a continuation, outflow boundary condition is applied. When w > ws, then w is set to w = We.

    In its simplest instance, this propagation law has the form Dn(K} = DCJ *(J - aK}, where DC.! is the Chapman-Jouguet detonation speed, and a is a constant related to the explosives ' detonation reaction-zone length . Thus, the wave either decelerates or accelerates depending on the sign of the curvature of the front. In addition , the speed of the DSD front is affected by the interaction of the front with inert material objects. This interaction involves a boundary condition on the DSD front. The angle between the normal to the detonation and the normal to the inert material surface, w, takes on a unique value, We, depending on the properties of the explosive and the inert. The boundary interaction is described in Figure 3 .

    Periodic Loadings of Spherical Particles

    To reduce the size of the calculations, we consider that the particle-loaded HE consists of a 3D, periodic array of uniform sized, cubic unit cells, of length L = 1 on a side. The test samples

    are built up by stacking these cells . Given the constraint of 20% by volume inert particles , the diameter of the particles is varied by changing the packing geometry of the spheres. To be consistent with the assumption that the detonation reaction-zone length of the HE is small compared to the particles, the DSD law is set to Dn = 1 - O.l -i

  • and y = 0, Z = 0) into an explosive sample of infinite extent.

    DSD Detonation Propagation Results

    T bl I a e < D 0> vs. geometry an db d oun ary ang e. OOc se Bee FCC

    0.785 =O.78 =O.71 =0.66 1.374 =0.86 =0.80 =O.77

    Two classes of initial-value problems were considered; a planar input along the bottom surface of the geometry shown in Figure 5 and a cylindrical wave input, whose axis is coincident with the lower left-hand edge of the Figure 5 geometry. From data for the detonation propagation problem with the initial, planar wave input, we determined the average, planar detonation propagation velocity, , displayed in Table I.

    Fig. 6. Time Ih = 5 isosurface for a detonation front, initially a cylindrical wave, with axis along the x-axis and r = 0.5, spreading into an infinite SCA inert sphere-loaded HE composite (wc = 0.785) as shown in Figure 5.

    Given the solution data from the propagation problem with the initial, cylindrical wave input, we were also able to determine the "effective" mean curvature dependence of the average detonation propagation law, = 0.803+/-0.003 (0.868+/-0.003) and = 0.156+/-0.004 (0.124+1-0.004) for the SC geometry and for the cases Wc = 0.785 (1.374). These values of are essentially identical to what is displayed in Table 1 for identical cases.

    3D Mesoscale Hydrodynamic Simulations

    What might be described as the standard approach to modeling a multiphase problem such as metal-loaded exp losive is two-phase, continuum mixture theory [1,9,10]. In that approach, the loading particles and the explosive are assumed to coexist at each spatial location, each phase is separately governed by its independent set of compressib Ie flow equations (Euler equations, typically), and the interaction between the phases is handled through a set of source terms to the equations (exchange terms) that describe the exchange of momentum and energy between the phases. A Ithough the modeling of those exchange terms is at the heart of the problem, the forms adopted for those exchange terms is carried over from simpler flows, like from the theory of incompressible low-speed flow over rigid particles [I]. That is particularly the case for the momentum interaction between the phases, wh ich is essentially modeled with some variant of a Stokes drag law. In the same (mesoscale) spirit as that we used to describe the detonation-front propagation problem, our objective here is to perform detailed interaction modeling of the high-speed, compressible detonation flow with the defined particles, and from those results, to then develop an "average" mean-flow description for the problem. That is, we seek to create the database needed in order to develop exchange terms appropriate for high-speed, compressible flow. To study the hydrodynamic loading of the embedded particles, we couple our detonation front propagation to the three-dimensional hydrodynamic flow simulation capability provided by the LLNL code, ALE3D [I I].

    As In our modeling of detonation propagation, we limit consideration to geometrically simple inert particle geometries; here the SCA geometry described above. We do this because the problem is fundamentally three-dimensional, and the numerical resolution of the flow must be adequate enough to resolve the details of the flow. Our geometry consists of a stack of I x I x I-unit cubes of explosive, stacked one upon another in the z-direction. At the center of each of these explosive cubes is a hollowed out spherical space containing a sphere of inert

  • material having a radius, r = 0.363. The lower most explosive cube contains only explosive. A two-dimensional plane cut of the geometry is shown in Figure 2. To have this stack of sphere containing explosive cubes in the z-direction act as a part of a semi-infinite sample (as in the previous sections), we apply symmetry boundary conditions along the bounding planes, x = 0, x = I, Y = 0 and y = I. Additionally, to maintain symmetry, we assume that an established, planar detonation wave enters our test sample along the plane z = 0, simultaneously at t = o.

    The initial set of problems we solve and report on here, restrict the number of length scales in the problem to just the unit length of a sphere edge and the fixed in itial radius of the sphere. We do this by assuming that the detonation is a Chapman-Jouguet (CJ) detonation, with a zero th ickness reaction zone (the fu II detonation energy release is triggered by the passage of the detonation shock) and with the detonation being fully supported at the CJ-state . This then corresponds to a CJ-state inflow boundary condition being applied at z = O. Then with the ratio of the explosive cell-edge length fixed, the sphere radius fixed and no explosive length scale, the problem time scales with /lDcl . The results we describe apply equally well to any system with this same ratio of dll = 0.363, which corresponds to a particle volume fraction loading of20%.

    Our explosive detonation model is the ABS model [7]. This model employs a constant gamma, y = 3, equation of state, an in itial explosive density of Po = 2 gm/cc and a

    , , Th detonation energy of q = 0.04 cm-/!-!s-. IS gives DCl = 0.8 cm/~ls and provides detonation characteristics like those in a solid , high-performance explosive. We use the Lund detonation lighting algorithm in ALE3D to propagate the zero-th ickness reaction-zone length detonation . At some point, we will introduce a detonation reaction-zone length scale and use a DSD lighting algorithm for these calculations. The currently implemented ALE3D DSD algorithm does not have a proper DSD boundary cond ition treatment, and thus would find no difference in the explosive confinement effect between a plastic, like Lucite, and a heavy metal, like tantalum.

    Mesoscale Hydrodynamic Simulation Results

    We consider four inert materials for the spheres, which span the range of loading material densities that could be considered of interest for applications: I) Lucite, 2) aluminum, 3) steel and 4) tantalum . In all cases, the materials do not react with the explosive products. The constituent response was taken from the ALE3 0 KO/SGEOS material library .

    Fig. 7. Four density palettes (different rainbow palettes for each case) are shown at t = 12.0 !-!s for the SCA I 0 problem. The I ines are the deformed boundaries of the original I x I x I-unit cells of explosive. From

  • top to bottom, the original inert spheres are Lucite plastic (rhoo = 1.182 gm/cc), aluminum (rhoo = 2.785 gm/cc), steel (rhoo = 7.90 gm/cc) and tantalum (rhoo = 16.69 gm!cc). In all cases, the detonation first reaches the right boundary, z = II , at t = 13.75 ).l.S. (See the Figure 2 legend for more display details.

    The SGEOS material model numbers are 37, 89, 28 and 77, for Lucite, aluminum, steel and tantalum, respectively [II]. A footnote on the ALE30 simulations we performed . We tried to import an interface conforming mesh/geometry into ALE30 from a Cubit hexahedral mesh, written as a genesis file. Our goal was to run the problem in ALE30's pure lagrangian mode. However, due to the large mesh distortions that occur in th is problem, it was necessary to switch to the A LE mode. Thus, there is little advantage to having a geometry conforming mesh. Here all the spheres were "shaped" into the geometry, and the material interface description was via ALE30's volume of fluid (VOF) mixed cell interface treatment approach. The explosive was burned using a programmed burn approach, with the total explosive energy release being over 1-2 computational cells. The programmed burn detonation state is very close to the exact computed detonation state for this model of PC! = 0.32 Mbar, uC) = 0.2 cm/).l.s, PC) = 2.667 gm/cc.

    Our goal is to use the simulation results to aid in the development of exchange laws for continuum mixture-type, two-phase models that are appropriate for metal- loaded explosives. To that el1d, we devised some diagnostics with which to measure spatial-averaged properties of this multi-material flow. Those diagnostics are based on doing instantaneous volume averages over the active parts of the flow (regions with pressure > 0.00 I Mbar) for each cell. We do separate bookkeeping for the explosive and inert material regions in each cell. Those diagnostics include the cell-volume averaged flow-involved volume, pressure, z-direction particle velocity (detonation propagation direction), and in the inert material region on Iy, the net d iss ipated energy (rate of entropy generation). We use the monikers "abscell#" and "insphere#" to separately label the explosive products and inert region parts of each cell. From left to right, the

    labeling for the explosive is abscell21, abscellll , abscelll2, . .. , abscell20, while the labeling for the inert is insphere I, insphere2, insphere3 . . .. , insphere 10. Thus, abscel121 is the left-most explosive-only cell, abscelill /insphere I is the following first explosive-inert cell, etc.

    A graphical summary of our results is displayed in Figure 7. These base-level simu lations used 50x50x550 computational cells. (We performed simulations at both half and double this resolution . Those results show only small quantitative differences.) As we go from top to bottom, the density increases, going from Lucite at the top to tantalum at the bottom. As expected, the Lucite "spheres" are more easily entrained in the flow than are the tantalum "spheres." What is clear is that once the detonation passes over a sphere, the spheres are deformed into other shapes; a convex shape for the Lucite and a concave shape for the tantalum. A Iso, note that the left boundary of each cell (being coincident with the original cell material boundary) mirrors the nature of the explosive products flow. Appropriate drag laws must reflect these facts . There are some interesting comments to be made with regards to acoustic impedance and sound speed in the inert materials and shock/detonation speed , but we reserve those for another time.

    Summary of Mesoscale Simulation Results

    In Figures 8, 9 and 10 we display the detai led cell-averaged results for the cell comprised of abscell13 /insphere3, composite ceH3 from the left.

  • ABSlucite 0.35 .----,.-..,---;-,-----,----,--.,.....---,

    0.3

    c: 0.25 os (I) E 0.2 > .J-.. E 0.15

    ~ 'l:i: 0.1

    0.05

    - p-abscel1J-vmean - p-lnsphere3-vmean

    !(f'S) Fig. 8. The volumemean (vmean) pressures in ce1l3 are compared in th is figure. The average over time of these pressures is nearly the same and slightly below PCJ . The Lucite pressure shows significant oscillations.

    ABSlucite 0.3 .----...-..,--r---r--,--,....---,

    0.25 c: ::: 0.2 E > ';;;'01 5 ::>.

    E ~ 0.1 '" ::>

    005

    '\ 1'",1 ~ '\ I ,....,.~ I I I-----::------j

    6 8 1'0 12 14 t(f's)

    Fig. 9. The vmean of the zdirection explosive products particle velocity is essentially UCJ of the neat explosive. The vmean of the Lucite particle begins by being above UCJ, reflecting the explosive drive into the central portion of this relatively low shock-impedance inert, and it then drops to near UCJ , as the particle deforms and its ' edges are pulled back (moved to the left) by the drag of the exp losive products.

    ABS-Iucite 0 .8 .----.-.---,r--.-...--,- -, 0.0002

    0,7

    0,6

    "H' 0.5 ~ o 0.4 ~ 03 .L . o > 0.2

    0.1

    0.00015 ...-..l.-__ ..:----'

    0,0001

    Fig. 10. This figure shows that: I) the overall volume of the cell is decreased, 2) the volume fraction of the Lucite is decreased due to the compression of the Lucite and 3) all of the entropy generated in the cell occurs during the time of shock/detonation passage through the cell. Thus, the oscillations in the Lucite pressure shown in Figure 8 are isentropic.

    The most striking observation in this example is the non-classical drag signature shown in Figure 9. The vmean particle velocity of the Lucite remains nearly constant and above UCJ until the drag forces applied to the particle, principally at its far outer surface, begin to deform the particle and slow it in the process. Thus, there is a delay, significant in length compared to the particle shock passage time, for which the vmean particle velocity of the Lucite remains constant before slowing in something that might be referred to as flow-induced drag. Also, it is noteworthy that all of the entropy generation in the Lucite occurs during shock/detonation passage . Otherwise, the flow is isentropic.

    The case for aluminum particles is similar to that for Lucite. Because of the difference in the shock impedance (higher shock impedance for the alum inurn), the vmean particle velocity in the aluminum is on a horizontal plateau below the UCJ speed of the detonation products, before it moves towards UCJ seven microseconds after the detonation passage time. Otherwise, the pressures are nearly in a non-osci llatory equilibrium, at a value that is slightly above PCJ . The volume fraction graph shows the same features as are shown in Figure 10 for Lucite.

  • Next we show the case for tantalum spheres. The case for steel is similar to that for tantalum except the behavior is somewhat muted.

    ABS-tantalum 0.5 r-- -----,-----,----,---,

    c m Q) E 0.3 > .......

    ro ~ 0.2 ~

    0.1

    t(~IS) Fig. I \. Although the vmean pressure in the explosive products and tantalum track one another, both pressures are seen to increase beyond PCJ . The pressure osci llations in the tantalum are significant.

    For the case of high shock-impedance tantalum, the flow in the particles is both non-isentropic and high ly deformational for the particles.

    ABS-tantalum 0.25 r--------...,.-r--r---,

    c

    '" Q)

    0.2

    ~ 0.15 ....... (j) ::. E 0. 1

    ~ N :::J

    0.05

    fi- 8- 1'o- 1'2- f4 t(ps)

    Fig. 12. The vmean z-d irection particle velocity begins well below the z-direction, vmean explosive products particle velocity, which is close to UCJ. The very low particle velocity in the tantalum is a consequence of the very high density and shock impedance of the tantalum. As one can see in Figure 7, the action of the detonation products flow accelerates relatively

    small amounts of tantalum around the outside of the particle in what is a shearing motion.

    ABS-tantalum 0.8 0.0007

    0.7 0.0006

    0.6 U 0.0005

    ~ 0.5 - - -s2-insphere3 ~

    r;. .:. (j) 0.0004 ~ 0.4 l i-e 0.0003 ~ 0.3 ..., III "C :::r > 0.0002 0.2

    0.1 0.0001

    0

    Fig. 13. The entropy production in the tantalum continues for an extended time, due to a strong shock-focusing effect in the particles. Th is results in a heating and a late-time expansion of the deforming tantalum particle.

    Conclusions from the Mesoscale Flow Study

    All of our results scale with the cell-edge particle dimension, I. We are currently developing an alternative momentum exchange description metal-loaded high explosives.

    References

    I. Frost, D. L., et a\., "Particle momentum effects from the detonation of heterogeneous explosives,"]. Appl. Phys., 101, 113529, 2007.

    2. Gogulya, M. F. and Brashnikov, M. A., "Detonation of metalized composite explosives," in Shock Wave Science and Technology Reference Library: Helerogeneous Delonalion, pp. 217-286, Springer-Verlag, Berlin Heidelberg, 2009.

    3. Frost, D. L., and Zhang, F., "Slurry detonation," in Shock Wave Science and Technology Reference Library: Helerogeneolls Delonalion, pp. 169-216, Springer-Verlag, Berlin Heidelberg, 2009.

    4. Ripley, R. c., et a\., "Shock interaction of metal particles in condensed explosive

  • detonation", in Shoek Compression 01 Condensed Matter, 2005 (M.D. Furnish, M. Elert, T.P . Russell, C.T. White, eds .), part I, pp.499-502 .

    5. Stewart, D. S., et aI., "Modeling unit cell interactions for the microstructure of a heterogeneous explosive: detonation diffraction past an inert sphere," in Shock Compression of Condensed Matter, 2009 (M. Elert, and W. Buttler, eds.).

    6. Robey, H. F., et aI., "Experimental investigation of the three-d imensional interaction of a strong shock with a spherical density inhomogeneity," Phys. Rev . Lett., 89 (8),085001-1,2002.

    7. Aslam, T. D., et aI., "Level-set methods applied to modeling detonation shock dynamics," 1. Comput. Phys. 126,390-409, 1996.

    8. Bdzil, 1. B., and Stewart, D. S. , "The dynamics of detonation in explosive systems," Annu. Rev. Fluid Meeh. , Vol. 39, pp 263-292, Annual Reviews, Palo Alto, CA,2007.

    9. Bdzil , 1. B., et aI., "Two-phase modeling of detlagration-to-detonation transition in granular materials: A critical examination of modeling issues," Phys. Fluids, 11 (2),378, 1999.

    10. Zhang, F., et al. "Explosive dispersal of solid particles," Shock Waves, 10,431, 200 I.

    ll. Nichols, A. L. 1[[, et aI., "User manual for ALE3D: An arbitrary Lagrange/Eulerian 2d and 3d code system," LLNL Report, LLNL-SM-404490,2009.


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