Analysis and Simulations of Low Power Plasma Blasting for processing Lunar Materials

8/14/2019 Analysis and Simulations of Low Power Plasma Blasting for processing Lunar Materials

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Analysis and Simulations of Low Power Plasma

Blasting for processing Lunar Materials

Martin E. Baltazar-Lopez1,Steve Best,2, Henry W. Brandhorst, Jr.3, Zachary M. Burell4

Space Research Institute, Auburn University, AL 36849-5320 USA

Matthew E. Heffernan5

and M. Frank Rose6

Radiance Technologies, Auburn, AL, 36849 USA

A prototype blasting power system suitable for excavation on the moons surface was

constructed and tested in the Space Research Institute (SRI) facilities. Such a system

incorporates the use of electrically powered plasma blasting via a blasting probe and

comprises a capacitor bank which is charged with a power supply at a relatively low rate

(e.g. a few seconds) and then discharged at a very high rate (power pulse of tens of

microseconds), generating a shock wave on a sample solid substance causing its fracture.

After successfully testing the blasting power system and blasting probes, breaking specimens

with masses of up to 850kg, 2-D and 3-D numerical simulations were carried out in order tocorrelate the experimental data of several samples of concrete cylinders. It is possible with a

non-linear hydro-code numerical approach to simulate the rapid discharge into high peak

power transient loads which eventually break the specimens.

Nomenclature

Pd= Power density

Ipk = Peak current

E = Voltage

V = Volume of reactant (blasting media)

I. Introduction

American Institute of Aeronautics and Astronautics

1

HERE is a need of numerical simulations of the plasma blasting event performed by a high peak pulsed power

conversion system in which a capacitor is charged over a long period of time at low current (power), and then

discharged in a very short pulse at very high current to break blocks of concrete or large rocks. Such a system for

excavation on the moons surface as well as scalable prototypes of plasma blasting probes for electrically powered

pulsed plasma rock blasting were developed and tested at the Space Research Institute (SRI) facilities. Several

experiments including blasting and fracturing of concrete blocks and granite rocks with masses up to 850kg were

performed.

T

Experimental testing can be expensive and time-consuming and plasma blasting is not exception. In

experimentation there could be things that go wrong when they are least expected, sometimes several tests are

needed in order to obtain a single valid data point. Thus numerical simulation can be used to complement and

validate the experimentation and once the simulation is validated it could even be used as an alternative to

experimentation within certain limits, with the corresponding savings in time and money.

1 Research Fellow, Space Research Institute, 231 Leach Center, Auburn University, 36849, AIAA Senior Member2 Research Engineer, Space Research Institute, 231 Leach Center, Auburn University, 36849, AIAA Member3

Director, Space Research Institute, 231 Leach Center, Auburn University, 36849, AIAA Associate Fellow4 Research Assistant, Space Research Institute, 231 Leach Center, Auburn University, 368495 Engineer, Radiance Technologies Inc., 231 Leach Center, Auburn University, 368496 Chief Technical Officer, Radiance Technologies Inc., 350 Wynn Drive, Huntsville, AL 35805, AIAA Associate

Fellow

7th International Energy Conversion Engineering Conference2 - 5 August 2009, Denver, Colorado

AIAA 2009-455

Copyright 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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The numerical methods used to simulate the blast effects problem typically are based upon a finite volume, finite

difference, or finite element method with explicit time integration scheme. In this work, a three dimensional

hydrocode is used to simulate the plasma blasting of concrete samples and some of the capabilities of these types of

codes to predict plasma blast loading are illustrated

II. 1Numerical Physics-Based Method

Hydrocodes can be used to simulate explosions and other high rate events. Most of the work on blastingsimulation using hydrocodes is aimed to study the effects originated by chemical explosives. For example, 2-D axial

symmetrical simulations for damage in blasted cylindrical rocks under explosive loading to analyze rock failure

mechanism was done by Zhu, et al.[1]. In another study, Plotzitza1 et al.[2] compare results of using mesh-based

hydrocode and a mesh-free Smooth Particle Hydrodynamics (MLSPH) method for 3-D simulation of concrete under

explosive loading.

Simulation of plasma blasting events has been done by Maldhaban et al.[3] with the purpose of characterizing the

plasma blasting in water and in another study by Pronko et al. [4] to determine power deposition and dynamic load

impedance based on the analysis of electric circuit characteristics. However, hydrocodes have been used very

incipiently for simulation of plasma blasting. In a study with a two-dimensional hydrocode SHALE, which is an

arbitrary Lagrangian Eulerian hydrodynamic code, Ikkurthi et al.[5] made simulations of crack propagation using a

crack growth and propagation model via the Bedded Crack Model (BCM). The study is limited to determining

fragmentation in one plane, thus it does not provide details which cannot be described in two-dimensional geometry

and can only be obtained from a 3-D simulation.Here we use AUTODYN [6] hydrocode for 2-D and 3-D simulation of plasma blasting events with the purpose of

getting an estimation of the damage of plasma blasting on concrete samples and then to validate those simulations

with experimental results. Once the code and simulations are validated, it will be possible to estimate blasting

damage on samples of concrete and other materials, saving the costs and time of experimentation, e.g., casting

concrete samples.

In solid mechanics problems, Lagrangian meshes have been used almost exclusively. Lagrangian meshes are

preferred for two reasons. First, as a solid deforms, its boundaries (if they initially coincided with an Eulerian mesh)

will no longer coincide with the Eulerian mesh lines, so complex procedures are needed at the boundaries. Second,

the stress-strain behavior and history of a solid is associated with material points, so that it is most convenient to

associate material zones in some manner with mesh zones. AUTODYN can handle both approaches selecting the

type of solver for a particular problem. The prescribed solvers in the code are Lagrange, Euler, Euler FCT, Shell,

ALE, or SPH. The choice of processor for each case is made according to the type of dynamic behavior expected.

For example, for gas or fluid dynamic behavior an Euler approach is typically utilized. For solid or structural

behavior, typically a Lagrange type of approach is chosen. The proper choice of processor type will provide an

accurate and efficient solution.

III. 2Power Density of Plasma Blasting

Even though evaluating the performance of materials under several conditions like burning, deflagration and

detonation is different, it is possible to compare them in terms of power density. The power density per unit volume

of reactant material for some specific events is given by Zukas and Walters[7] in W/cm3. For comparison purposes,

the power density in the case of plasma blasting can be calculated taking into account the energy spent at the plasma

blasting probe. For example, if the electrode separation in the blasting probe is of 1 inch, the blasting media

occupies the volume between the bottom of the borehole, the ground electrode and the blasting tip. The estimated

volume, completely filled with blasting media is 4.83cm3, which is also in accordance with the spherical volume

considered by Ikkurthi et al. [5] to estimate plasma blasting pressure levels. Based on those typical values, a power

density per unit volume can be calculated as follows:

V

EIPd

pk= 1

Hence, to obtain the maximum power at 52kJ assuming a system charge with 16kV, from the experimental time-

history data, the voltage spent at the blasting probe is multiplied times the measured peak current; this gives a power

of 758MW. This value is then divided by the volume of reactant blasting media for a total power density of 157

MW/ cm3. This value is in agreement and within the range of values calculated by Pronko et al. [4], and then we can

say that a typical blasting test with the SRIs plasma blasting system could provide a power density of 150 MW for


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an initial energy charge of 53kJ and for the actual volume of blasting media contained between the borehole and the

blasting probe.

As it can be observed in Table I, plasma blasting, compared to burning, and deflagration has higher power density,

but it is not as high as that of high explosive materials. However, is it is shown later, because the very high loading

rate, the results of plasma blasting can be compared to those of high explosives, this is also true because

performance is dependent on the velocity of detonation among other variables.

Table I. Power Densities for various events.

Event Power density KW/cmBurning Acetylene 10-1

Deflagrating propellants 103

Plasma Blasting 105

Detonating high Explosive 107

IV. 3Experiments

After successfully blasting concrete specimens without any reinforcement we proceeded to test a set of samples to

include the steel wire reinforcement and granite rocks with the purpose to emulate rocks and lunar soil. The steel

wire mesh used was 2 wrapped layers of 0.125 steel wire welded mesh of 6 x 6 spacing. The test setup is shown

in Figure 1.

.

Figure 1. Test setup characteristics of 24 dia. X 36 long, steel-reinforced concrete

c linder sam le.

The concrete cylinders were blasted using a 12 deep plasma blasting probe. The probe had 1 electrode gap. Un-

reinforced concrete of this size were easily shattered and scattered about the lab. This time the steel accomplished its

purpose of reinforcing the concrete sample, and it fractured and cracked in many pieces. As can be observed in the

top part of Fig.2, the cracks extended in some cases all the way down the height of the sample, and others down the

distance approximately equal to the depth of the borehole. The radial cracks on the upper surface tended to form thenow usual quadrant shapes.


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Another test series corresponded to similarly sized steel-reinforced concrete cylinders, but now blasted using a

short 6 plasma blasting probe. As can be observed in the bottom part of Figure 2, the effect had some surface

spallation. This blast was characterized by a considerable zone of crushing around the borehole, in this case with

cracks extending up to the walls of the cylinder. The number of radial cracks and cracks to the side walls also

increased though the gaps in the cracks were smaller compared to those of the 12 blast probe test. Most of the side

crack went down approximately 9.5, or 3.5 lower than the blast probe implying an average lateral crack angle of

approximately 16 degrees. The energy calculations from the time-history waveforms corresponding to this series of

tests, can be found in previous work[8,9].

Figure 2. Steel-Reinforced concrete cylinder 6.2 ft

3

(0.17m

3

) after blast test (a) with12 Probe and (b) with 6 probe.

(b)

(a)


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Figure 3. Granite rock, before and after blast test shot with 12 Probe.


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4V. Simulations

2-D simulationsSeveral plasma blasting computer simulation scenarios were run and examined on 24 dia. x 36 long, steel-

reinforced concrete cylinder with 60s energy pulse width and 12 probe. The reason for developing computer

simulation capabilities was to see if this could be a viable option to help us examine future application and

techniques for plasma blasting prior to conducting real physical laboratory tests. Actual laboratory blast tests would

be compared to a comparable series of simulated plasma blasting runs of a large perimeter-reinforced concrete blockat various depths and blasting pressure.

In computer simulations we assume an initial energy charge of 53kJ. The electrical basis for these simulations

corresponds to the experimental sample blasted in a typical test where it was observed that the current pulse is

delivered in approx. 60s. This suggested the pulse or energy deposition interval to be used as a starting value for

the simulations.


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Due to the absence of proper physical model for arc power deposition or

pressure measurements, it is considered that the peak pressure in the plasma

blasting zone is a hydrostatic pulse. Then we simulated the blast loading by

applying stress boundary conditions to the borehole faces within the blasting

zone. This approximates the loading experienced in a real cylinder with a blast

probe electrode gap of 1. Considering that energy is being delivered to the

blasting media precisely when the current flowing through it is a non-zero value,

the loading rate was estimated from I-V time-history traces obtained duringactual testing. In our simulations we included a loading rate with a pulse profile

of the form of an underdamped harmonic oscillator, with peak amplitude of

600Mpa and duration of 60s, which is representative of what we saw in

experiments. The Lagrangian solver of the code was used to solve the 2-D axial

symmetric model with 31,350 elements. A Porous EOS for concrete was

integrated with activated stochastic failure. The original solution is half of that

shown in Fig. 4, then it is mirrored to complete the view.

We did more simulation varying the energy deposition pulse widths including

50s, 60s, 75s, 100s, 125s, 150s, 200s, 250s, and 300s and we could

observe that the longer deposition time, the less damage immediately around the

blasting zone. However according to the simulations, the direction of cracks and

extension of damage varies. For lower times the damage is concentrated in the

central portion of the cylinder with cracks extending towards the top and bottom parts almost vertically in a short

distance after some initial quasi radial direction. For slower (longer) pulses, or energy deposition pulse widths, thecracks are extended towards the exterior in a 45 degree pattern forming conic cracks up and down, appearing as an

X in cross-section. This suggests that the damage is greater in the top part than in the bottom with shorter pulse

widths.

Figure 4. Result after 300s

simulation in a steel-

reinforced concrete sample.

Energy deposition rate 60s

3-D simulations

The use of 2-D axial symmetry is a computationally efficient way to simulate the loading of a 3-D cylinder.

However it does not show the complete solution of true dynamic fracture and fragmentation of specimens during

and after the plasma blasting and full three-dimensional analysis is necessary to obtain the actual solution.

The three-dimensional Lagrange processor in

AUTODYN-3D is based on the approach derived in HEMP-

3D by Wilkins et al [10] and is an extension to the 2D

processor. The Lagrange coordinate system can

accurately follow particle histories, and thereforeaccurately define material interfaces and also follow stress

histories of material in elasticplastic flow. Materials are

defined on a structured (I, J, K) numerical mesh of six sided

brick type (hexahedral) elements, Fig. 5, and the eight nodes

(one on each vertex), of the mesh move with the material

flow velocity. Material stays within the element in which it

originally lay.Figure 5. Hexahedral element showing the I-J-

K convention of nodes[11].The partial differential equations to be solved express the


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conservation of mass, momentum and energy in Lagrangian coordinates. These, together with a material model and

boundary conditions, define the solution of the problem. Material associated with a Lagrangian zone stays with that

zone under any deformation. Thus a Lagrangian grid moves and distorts with the material it models and

conservation of mass is automatically satisfied. Details of governing equations are found in the AUTODYN Theory

Manual[11].

Because of symmetry, only half cylinder was modeled. The particular cylindrical shape of concrete with a

borehole was formed with a two-part model. The two parts were joined as shown in Fig. 6.

In this case the models were solved with Lagrangian solver and also could be solved using the ALE solver. The

dimensions of the cylinder are 36 long, 24 diameter with a borehole of 1 diameter. The solid model had a total of

260,344 nodes, the simulation solution time ended at 300s, and the pressure loading condition was 600MPa with a

pulse width of 60 s to emulate the plasma blasting. This simulation took approximately 3 hrs to run using a dual

core processor @ 2.2GHz, 2GB of RAM.

In blasting of concrete, the mechanisms of

material failure and damage occur by the sudden

growth of cleavage cracks. The response of the

material is then a loss of strength that leads to the

failure. The softening response after the peak load

is a structural response to the damage, and should

not be considered as stress-strain curves for the

material.

The code implements complex constitutiverelations for non-homogeneous materials such as

soils, rocks and concrete. To model the behavior of

concrete, a Porous Equation of State (EOS) is used

and the strength model implemented is a Drucker-

Prager strength model which is a pressure-

dependent model for determining whether a

material has failed or undergone plastic yielding. It

was determined that the Drucker-Prager criterion

gave the best results for this application based upon previous physical observations of the plasma blasting

experiment samples. The Drucker-Prager failure model, with a porous EOS was chosen as the best combination of

failure model and equation of state for these simulations. The other options used were the RHT concrete model EOS

and the Johnson-Cook failure mode. The RHT (Riedel, Heirmaier, and Thoma) concrete model EOS, which has its

own associated RHT-failure model, produced results inconsistent with what was observed in our experimentalplasma blasting. We had begun computer simulations with the RHT model, but once we worked through symmetry

issues, the RHT model produced anomalous results giving damage between 0.95 and 1 in greater than 50% of the

sample which is obviously not what we see experimentally. Similar unacceptable results were obtained when using

the Johnson-Cook failure mode. The porous EOS with Drucker-Prager failure model produced results very, very

similar to what was actually seen in experimentation.

Figure 6. Model with two joined concentric cylindrical

parts.

One approach to simulating the response of concrete is to explicitly model the mechanisms of damage and failure

in the material. The program has the option to present the results in terms of damage with a relative scale going from

zero to one, and graphically with a scale of colors. Also it is possible to specify stochastic failure mechanism in

concrete to take into account the heterogeneities in the material. Values of the Bulk modulus, and the ultimate

compressive strength of concrete were obtained from bench tests.

5VI. Results

Comparison of the simulation and the experiment

We reviewed and compared some observations made between computer simulations of concrete blasting with

physical observations after cutting open one of the perimeter-steel wire reinforced cylindrical concrete blocks which

had been previously blasted and saved for this comparative analysis.

When the results from the simulation are compared to the experiment, Fig. 7, it is evident that there is more

similitude than difference on the shape and trends of line cracks. For the 12 inch probe sample, the cracks started

extending from the initial area of blast in approx. 40 degrees continuing towards the upper part almost vertically.

Located at approx 20 degrees down from the horizontal a medium crack developed extending radially from the


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center. Another set of cracks developed downward mainly in two lines one directed almost vertical to the bottom

and another one in approx 45 degrees.

Highlighting the cracks on the picture and comparing side to side with the simulation, it can be observed that the

simulation fairly well corresponds to this particular experimental concrete sample blasted with initial energy of

53kJ, a total net energy used in blast of 26.7kJ, and a deposition in 60s. At this point we could say that the

simulation is reasonably validated with the experiment.

Crack Growth


7

Preliminary results of damage and crack growth in 2-D

simulations demonstrated congruence between numerical

and experimental results for blasts performed on 12 and

18 concrete cylinders[9]. The loading process to the

concrete during electro-hydraulic blasting divides in two

basic loads. There is the initial shock wave blast on the

inside of the borehole which initiates cracking in the

sample. This is followed by a slower loading phase from

the expanding hot gases which penetrate and evolve the

cracks initiated during shock wave loading.

As in the case of 2-D simulations, in the 3-D simulations

we only investigate the shock wave loading due to stress

exerted inside the borehole in order to understand how

loading rates determine the initial cracking pattern. We alsoassume that the peak pressure and pulse duration are based

upon spherical source geometry with symmetric

propagation of the pressure wave. The plot of the pressure

pulse detected by a virtual gauge in the model is shown in

Fig. 8.

Figure 7. Comparison of simulation and

experiment of a blasted 24 in reinforced concrete

cylinder.

The resulting crack propagation and damage after 300s

simulation time is presented in Figure 9 and it is compared

to the result of the 2-D simulation under same conditions.

The resulting red zones represent a fragment path with

material reduced to small rubble which has totally lost its

strength.

Yellowish lines emanating from the rubbled zone represent cracks. Figure 9 indicates that almost symmetrical

crack growth occurs on both sides from the blasting hole, forming the X shaped crack pattern which also was

observed in the 2-D simulations.

Figure 8. Time-history of the pressure pulse as detected

at a point near the hot zone

Figure 9. 24x 36 cylindrical concrete sample

models after 300s simulation time of a 600MPa

blast @ 60s pulse width, (a) y-plane view of 3D

simulation and (b) 2D simulation


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A quasi horizontal fragment path develops passing through the center of the X shape. Cracks located at the mid

length on each leg of the X shape developed in vertical direction, this trend was noticed in the 2-D simulations

too. Note that in the 2D simulations the symmetry is perfect because the original simulation was for half of the

model and the result is mirrored along vertical axis to complete the model.

A sequence of time-history of cracks and damaged zones is shown in Fig. 10.

Figure 10. Crack propagation sequence after blasting simulation with 600MPa pulse.

Sliced view planes of damageThe 3-D solutions can be represented in cut-out sliced plane views along radial and longitudinal directions. This is

useful to verify the symmetry (or lack of symmetry) of cracks and damage along different radial planes and

longitudinal (transversal) planes. In Fig. 11 the slices of radial cut-out planes of the concrete sample blasted with

600MPa and 60s pulse width are seen. The slices were taken each 15 degrees angular separation. As can be

observed, those slices varied from one angle to the other, which at first view, is in concordance with the

experiments. Note that for view separated each by 45 degrees, approximately repeated patterns are observed.


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The second part of this analysis consisted of virtual transversal cut outs to get sliced planes in the longitudinal

direction in order to inspect the variation of damage at distance step intervals of 0.5 or 1 each from the bottom. As

can be seen in Fig. 12, the damage level varied across the length of the model, being more intense near the bottom of

the blasting hole. These sliced planes confirmed that the stochastic nature of the material definition worked fine to

emulate the heterogeneity of concrete as it produced non-symmetric results in the three-dimensional simulation.

300 15

45 60 75 90 105

120 135 150 165 180

Figure 11. Sliced planes along radial direction of concrete sample blasted with

600MPa and 60s pulse width after 300s simulation.


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Figure 12. Sliced Planes along longitudinal (transversal )direction of concrete sample blasted with

600MPa and 60s pulse width after 300s simulation. The distance indicated is from the bottom ofthe sample.

6VII. Conclusion

Experiments of plasma blasting on concrete and granite rocks were performed with the purpose to emulate rocks

and lunar soil. Two and three dimensional simulations of plasma blasting on concrete samples were performed. In

general, it was shown that the mechanisms of damage and failure of plasma blasting can be simulated by hydrocodes

and the solutions are very congruent with the experimental results. The heterogeneous nature of concrete samples

blasted with 600MPa and 60s pulse width was numerically verified by the asymmetry of cracks and damage along

different radial and longitudinal (transversal) planes.

It is possible to analyze various structural response situations including damage and failure over a wide range of

loading conditions without the need of setting up an experimental rig for each analysis, realizing a savings in time

and experimental costs.

7VIII. Acknowledgements

This work was supported under NASA Contract No. 07-060287, Highly Efficient High Peak Power ElectricalSystems for Space Applications funded through Radiance Technologies, Inc.

Any opinions expressed are those of the authors and do not necessarily reflect the views of NASA.

8IX. References

1. Zhu Z., Xie H., Mohanty B., Numerical investigation of blasting-induced damage in cylindrical rocks,International Journal of Rock Mechanics & Mining Sciences, 45 , 111121 2008.


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2. Plotzitza1 A.; Rabczuk T.; and Eibl J., Techniques for Numerical Simulations of Concrete Slabs forDemolishing by Blasting, Journal of Engineering Mechanics, Vol. 133, No. 5, 523-533, May 1, 2007.

3. Madhavan, S.; Doiphode, P.M.; Chaturvedi, S.; Modeling of shock-wave generation in water by electricaldischarges,IEEE Transactions on Plasma Science, Volume 28, Issue 5, 1552 1557, , Oct. 2000.

4. Pronko, S.; Schofield, G.; Hamelin, M.; Kitzinger, F.; Megajoule Pulsed Power Experiments for PlasmaBlasting Mining Applications. Ninth IEEE International Pulsed Power Conference, Vol. 1,15-18, Jun 1993.

5. Ikkurthi V. R., Tahiliani K., Chaturvedi S., Simulation of crack propagation in rock in plasma blastingtechnology, Shock Waves, 12: 145152, 2002.

6. Century Dynamics Inc., ANSYS AUTODYN Explicit Software for Nonlinear Dynamics, User Manual,Ver. 11, 2007.

7. Zukas J.A., Walters W.P., Explosive Effects and Applications, Springer-Verlag, 1997.8. Best S., Baltazar-Lpez M. E., Burell Z. M., Brandhorst, H.W., Heffernan M. E., Rose M.F., Pulsed

Powered Plasma Blasting for Lunar Materials Processing, IEEE 35th International Conference on Plasma

Science, ICOPS 2008, Karlsruhe, Germany, 2008.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4591195

9. Best S., Baltazar-Lpez M. E., Burell Z. M., Brandhorst, H.W., Heffernan M. E., Rose M.F. ,A LowPower Approach for Processing Lunar Materials, 6th International Energy Conversion Engineering

Conference (IECEC), Cleveland, Ohio, 28 - 30 July 2008.

http://pdf.aiaa.org/preview/CDReadyMIECEC08_1836/PV2008_5710.pdf

10. Wilkins, M. L., Blum, R. E., Cronshagen, E. & Grantham, P. , A Method for Computer Simulation ofProblems in Solid Mechanics and Gas Dynamics in Three Dimensions and Time. Lawrence LivermoreLaboratory Report UCRL-51574, 1974.

11. Century Dynamics Inc., AUTODYN Explicit Software for Nonlinear Dynamics, Theory Manual,Revision 4.3. 2005.
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4591195http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4591195http://pdf.aiaa.org/preview/CDReadyMIECEC08_1836/PV2008_5710.pdfhttp://pdf.aiaa.org/preview/CDReadyMIECEC08_1836/PV2008_5710.pdfhttp://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4591195

Analysis and Simulations of Low Power Plasma Blasting for processing Lunar Materials

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