Analysis of interaction occurring between space debris and orbiting structures is of great interest to the planning and survivability of space assets. Computer simulation of the impact events using hydrodynamic codes can provide some understanding of the processes but the problems involved with this fundamental approach are formidable. First, any realistic simulation is necessarily three-dimensional, e.g., the impact and breakup of a satellite. Second, the thickness of important components such as satellite skins or bumper shields are small with respect to the dimension of the structure as a whole, presenting severe zoning problems for codes. Thirdly, the debris cloud produced by the primary impact will yield many secondary impacts which will contribute to the damage and possible breakup of the structure. The problem was approached by choosing a relatively new computational technique that has virtues peculiar to space impacts. The method is called Smoothed Particle Hydrodynamics

Allahdadi, Firooz A.

Carney, Theodore C.

Libersky, Larry

English

NASA Technical Reports Server

N92-22380
Simulating Hypervelocity Impact Effects on Structures
Using the Smoothed Particle Hydrodynamics Code MAGI
Lar_ Libersky
('enter fiJr FSxplosives "lechnololo' Research
New Mexico Itt_'titute of Technology
Sc_'orro, NM. 87801
Firooz Allahdadi
Phillips Laboratory
Space Kinetic" Impact & Debris Branch
Kirtland AFB NM. 87117
Theodore C Carney
Advanced Sciences lnc,
6739 Academy Road NE.
Albuquerque, NM. 87109
INTRODUCTION
Analysis of interaction occurring between space de-
bris and orbiting structures is of great interest to the
planning and survivability of space assets. Computer
simulation of the impact events using hydrodynamic
codes can provide some understanding of the pro-
cesses but the problems involved with this fundamen-
tal approach are formidable, First, any realistic simu-
lation is necessarily three-dimensional, e.g., the
impact and breakup of a satellite. Second, the thick-
ness of important components such as satellite skins
or bumper shields are small with respect to the dimen-
sion of the structure as a whole, presenting severe zon-
ing problems fi)r codes. Thirdly, the debris cloud pro-
duced by the primary impact will yield many secondary
impacts which will contribute to the damage and pos-
sible breakup of the structure. Characterization of the
debris cloud requires accurate fragmentation model-
ing as well as accurate tracking of the fragments
through large regions of void. For these reasons hy-
drodynamic simulation of hypervelocity impact and
breakup of orbiting structures is extremely difficult.
We have approached the problem by choosing a rela-
tively new computational technique that has virtues
peculiar to space impacts. The method is called
Smoothed Particle Hydrodynamics (SPH). In this pa-
per we describe the SPH method and why we believe
that it can be used to answer many questions concern-
ing the survivability of space assets due to kinetic ira-
pacts. We also present several calculations to show the
power of SPH towards such problems.
SPH BASICS
Smooth Particle Hydrodynamics is unique in
computational fluid dynamics in that SPH uses no
grid. It was the genius of the inventors, Lucy (1977)
and Gingold & Monaghan (1977) to figure out how to
take a derivative (get the force on a fluid element)
without using a mesh. Previously a mesh was the only
known way to compute a spatial derivative using fi-
nite differences. The mathematical theory of SPH
will not be discussed here. The reader is referred to
Gingold & Monaghan (1977,1982), Monaghan
(1982,1985) and Monaghan & Gingold (1983) for de-
tailed treatment of the subject. We present here only
some basic features as discussed by Benz (1989) that
are necessary to understand the method. Consider a
function f, a kernel W which has a width measured by
the parameter h, and the following equation:
f
< f(r) > = / W(r- ' h'_'r ....r, y( )ar. (1)
J
If we impose a normalization condition such that the
integral of W is unity, then it follows that
h--,0
< fir) > --" fir) . (2)
763
https://ntrs.nasa.gov/search.jsp?R=19920013137 2020-03-17T12:03:59+00:00Z
Relation (1) therefore defines the kernel estimate <f>
off. If W is the Dirac delta function then we have the
equality <f>=f. Now suppose f is known only at N
discrete points that are spatially distributed according
to the number density distribution:
N
n(r) = 2 6(r- rj), (3)
j=l
If the number density at rj is written as
Q(rj)
< n(rj) >- (4)
mj
thus introducing the concept of particle mass (m), the
following equation can be derived:
< f(r) > =2 fJ W(r-rj 'h) mj (5)
This equation defines a procedure for transforming
integral equations to particle equations and is
therefore called "integral evaluation by the particle
method." The choice of kernel or "smoothing
function" is discussed by Monaghan and Lattanzio
(1985). The W most frequently used in SPH codes is
a B-spline with compact support which goes to a zero
at a distance 2h from its peak. When the conservation
laws of fluid dynamics are cast into the SPH
framework using the procedure described above, the
following equations are obtained.
)
dt LO;+ + m, fw, j
o7 (7)
dei _ Pi
J
1
+7Z ,r,)
J
(8)
Equation (6) is the density computation of particle 'T"
using the masses of neighboring "j'" particles. The ac-
celeration of particle "T" is given by (7) and the evolu-
tion of the specific internal energy (e) is described by
equation (8). These equations also involve the pres-
sure (P) and the artificial viscous pressure 1-1. Terms
involving material strength are omitted here but are
discussed by Libersky and Petschek (1991). It should
be emphasized that equations (6) thru (8) are the con-
tinuum equations of fluid dynamics cast into a discrete
Lagrangian frame by kernel interpolation. Therefore,
the Smoothed Particle Hydrodynamics method is a
true and complete hydrodynamic calculational proce-
dure.
IMPORTANCE TO SPACE IMPACTS
Simulating the mechanics of irreversible processes
that take place between a structure and a projectile
during a hypervelocity collision in space is extremely
difficult. There are three main reasons for this. First,
problems are three-dimensional. Second, the thick-
ness of important components such as satellite skins.
electronic components or bumper shields are small
with respect to the dimension of the structure as a
whole. Three-dimensional calculations using mesh-
based codes do not seem feasible for such problems.
Thirdly, the debris ch)ud produced by the primary im-
pact produces secondary and tertiary impacts impor-
tant to the overall damage and breakup. Simulation
of these events requires detailed characterization of
the debris cloud which in turn requires good fragmen-
tation modeling as well as accurate tracking of the
fragments through large regions of void. Eulerian
codes have difficulty tracking sub-grid scale frag-
ments through the mesh. Also, large regions of void
within the structure need to be zoned in anticipation
of material arriving there at some later time. SPH suf-
fers from neither of these difficulties because there is
no mesh. Following the debris cloud through large
regions of wild presents no difficulty to SPH. Further-
more, interfaces between materials in a problem con-
sisting of several materials are accurately tracked.
These virtues of SPH are true of any Lagrangian code,
except that mesh-based Lagrangian codes cannot
treat large fluid distortions. Obviously, hypervelocity
impact produces highly distorted flows. It can be said
764
that SPH ccmtains the best features of grid-based Eul-
erian and Lagrangian methods without the limitations
of either. The price to be paid is that SPH is slower
than the other methods, (having to determine new
neighbors each computational cycle) but not prohibi-
tively so. The efficien W of SPH appears to be much
better than Eulerian in 3D (Durisen, 1988) and we are
paying close attention to vectorization and paralleliza-
tion. The ability of SPtt to accurately track debris re-
suiting from hypervelocity impact through large re-
gicms of void in 3 dimensions and compute the impact
of the debris on other parts of the structure make the
method extremely attractive for space applications. In
working towards that goal we have performed several
two-dimensional calculations to evaluate SPIt and get
a feel for how impact events might damage and lead
to breakup of the large-scale structure.
SYNTHESIS OF A PREDICTIVE BREAKUP
MODEL
Determination of processes that contribute to the fail-
ure and ultimately to the breakup of a complex and in-
tegrated space asset under impulsive loading is of vital
interest, fTurrently, such a predictive model does not
exist. Until recently, virtually all breakup modeling of
a spacecraft under intensive loading used a phenome-
nological approach. Although this approach provides
some qualitative measure of the interactions, it lacks
the physics necessary to identit_¢ those processes that
control generation of the resulting debris cloud, qb
characterize the environment of a debris cloud accu-
rately, (in terms of debris mass, velocity and number
distribution), a first principles physics based predictive
model has been synthesized. This approach considers
the synthesis of a total predictive model based on the
response of elementary components. Internal compo-
nents of a generic satellite are shown in Figure 1 and
an example matrix of calculations leading to the total
predictive model is shown in Figure 2. The design of
these and other calculations is motivated by the vari-
ous geometries of the components inlernal to the sat-
ellite. "l_,'o simulations of local impact events on small
regions of a large scale structure are shown in Figure
3 and Figure 4. These calculations give us detailed un-
derstanding of how the debris cloud interacts with
nearby structural elements producing damage.
Figure 3a is a particle plot showing initial conditions
for the impact of an tantalum projectile on an alumi-
num (2024-T86) frame. Each arm of the frame had
length 20.5 cm and thickness 0.5 cm. The projectile
had 1.0 cm sides, a speed of 7 km/s and a 60 degree
impact obliquity. The calculation was performed in a
two-dimensional Cartesian frame of reference. A
Gruneisen equation of state and an elastic-perfectly
plastic constitutive model were used to describe the
metals. The calculation used 12,240 particles and the
smoothing length was 0.08333 cm. Results of the cal-
culation at 1 and 20 microseconds are shown in Fig-
ures 3b and 3c respectively. A very large opening is
created in the first plate impacted due to the large im-
pact obliquity. This "hole'" is approximately 7 times
the initial projectile size. One end of the plate is bent
inward. There is a large splash of material moving up-
ward and away from the structure typical of high speed
cratering events and a debris cloud expanding towards
the other arm of the structure. This cloud has frag-
ments of various sizes but most of the mass is concen-
trated in the part of the cloud that is about to impact
the second structural arm.
Results of a similar calculation employing a slightly
more complex aluminum structure are displayed in
Figure 4 where particle plots at four different times (0,
10, 20, 30 bts) are shown. In this calculation the debris
cloud, resulting from the impact upon one member of
the aluminum frame, is seen impacting other structur-
al elements. Severe damage is seen on the upper pan-
el. In fact, a secondary debris cloud has been pro-
duced by the interaction. It is easy to see from this
calculation, that in an actual satellite with many more
composite parts, how a cascade of debris clouds could
form to cause massive breakup of the structure. Some
damage is also seen on the outside panel furthest from
the impact. These calculations were performed on a
1 megaflop machine and required approximately 1
hour of cpu time per 10 las of simulation time.
765
Target Name: chucksat.tp4
Aimpoint(X,Y,Z) (cm) = ( 0.00 0.00
Observer Azimuth (degrees) = 91.00
Observer Elevation (degrees) = 0.00
45.5O)
/ \
Figure i. A Generic Satellite
766
Figu[e IA. Inte[io_ Components of Satellite
767
i,'2cm
Matrix of Calculations Lad,n ° to a
Satellite Breakup Model
I/4 C,_. [,_2 cm
2D Cyii,'sdrica] (29) I cr_
3D Cartcma;: (3.6)
2D Cylindrical
(2.!0)
3D Car[csian
(?.7)
1,4 cnt
gap
%\_ 3D Ca;waian(3.9)
All matcriala _6 atumu',um
(2.22)
38 cm gap
3D Cartcaian
(3.8)
35 on; gap
3D Cagtcsiaii] /_
//
Figure 2. Matrix of Calculations
768
• _J0
I
!
(3a) Initial configuration.
(31)) i microsecond after initial impact.
E"i l'_ e 3,
}laterial plot of a _antalum projectile penet1x', !:_ S an alL_'.J:',,_:TI
L_-_t_!e ,it 60 ° obliquity.
769
h
I
f
(_<: ['[: J::ictosccoi_c!s af[er initial inpacu
[']LSult 2 (c<);t[ : "l:lt<,rial plot of a tantalum ptoj<:cuil<_ ]_e:_etra[]l,f,, ::
aluJ;_i;nn:: frame at 60 ° obliquity.
770
30
Material Plot
Time = 20.0 micro-sec
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
:!i¸
-_._.... _ii__
,.,..
0 5 10 15 20 25 30 35 40 45 50
30
28
26
24
22
20
18
1416_ .....
12
10
8
6
4
2
0
O 5 10
Materlal Plot
Time = 180.0 mlcro-sec
ii;
_.,_,. iilii_ii/_[':
1,5 20 25 30 3.5 40 45 50
5O
28
26
24
22
20
18
16
14 ..........................
12
10
8
6
4,
2
0
0 5 10
Material Plot
Tfme = 324.9 mlcro-sec
/
",%.
15 20 25 30 35 40 45 50
30,
Materlal Plot
Time = 647.0 mlcro-sec
26
24
22
16 _--_
14 r- '_..........
12L
d
10L8 %,-- ..... ,4 h_.
0 ........................... 2_. :i ..................
0 5 10 15 20 2,5 30 3.5 40 4.5 50
Figure 5. Smoothed Particle Hydrodynamics simulation of a liquid filled
steel pellet impacting multiple spaced plates at 2 km/s and high obliquity.
The first plate impacted is aluminum amd the remaining two are steel. The
calculation was done in two-dimensional Cartesian coordinates using the
SPH code MAGI. Frames a - d show results at 20, 180, 325, and 647 Its.
771
25
2O
15
10
5
0
-5
-1(
-1
-2.' :"-'" ............................................
0 5 10 15 20 25 30 35 40 45 50
2.0000E-01 1 .8000E+O0
Density (_I/'c c)
ime = 30.0 micro-sec
20 b
15
10
5
:....0
-5
-I0
-15
-20
-25o 5'
Z_
2.oooo£-olDensi f y (_/_gO_E,O0
Time = 120.0 micro-sec
25
2o
15
-20
-25
0 5 10 15 20 25 30 35 40 45 50
2.0000E-01 1 .8000E+O0
Figure 6. Smoothed Particle Hydrodynamics simulation of a liquid filled
aluminum tank hit by an aluminum projectile moving at 7 km/s. The
calculation was done in two-dimensional Cartesian coordinates using the
SPH code MAGI. The liquid particles are gray-scaled by density and the
aluminum particles are shown in black. Frames a-d show results at 3, 30,
60, and 120 _ts.
772
Several calculations have been presented - two hyper-
velocity impacts on simple structures, and two other
impact problems possessing interesting features. We
are encouraged by the results. The code has been ex-
tended to three-dimensions and we are currently per-
forming test problems.
REFERENCES
Benz, W., Numerical Modeling of Stellar Pulsation:
Problems and Prospects, Nato Workshop, kes
Arcs, France, March, 1989 (Harvard Smithsonian
Center for Astrophysics, Preprint No 2844, (1989).
Durisen, R.H., R.A. Gingold, J.E. Tohline and A.P.
Boss, The Astrophysical Journal, 305, (1986),
281-306.
Gingold, R.A. and Monaghan, J.J., Mon Not Roy
Astron Soc 181 (1977), 375-389.
Gingold, R.A. and Monaghan, J.J., J Comput Phys 46
(1982), 429-453.
Libersky, L.D. and A.G.Petschek, Lecture Notes in
Physics, Springer Verlag, in print (1991).
Lucy, LB. Astron. J. 83 (1977) 1013-1024.
Monaghan, J.J., SIAM J Sci Stat Comput., 3 (1982),
422.
Monaghan, J.J., Comp Phy Rev 3 (1985), 71-124
Monaghan, J.J and Gingold, R.A, J Comput Phys 52
(1983), 374-389.
Monaghan, J.J. and Lattanzio, J.C., Astron Astrophys
149 (1985), 135-143.
773
ADDITIONAL IMPACT CALCULATIONS
Two additional calculations are presented in order to
show the power of SPH towards impacts. Figures
5a-5d are particle plots showing a liquid filled projec-
tile impacting a series of spaced plates at high obliqui-
ty. The projectile casing was steel and the simulated
liquid was modeled as carbon-tetrachloride. The
length of the projectile was 3.75 cm and the thickness
2.50 cm. The first plate to be impacted was aluminum
with thickness 0.254 cm, and the remaining two plates
were steel with thicknesses 0.48 cm and 1.58 cm re-
spectively. The projectile speed was 1.6 km/s. The
problem was run in a two-dimensional rectangular
Cartesian frame of reference (plane-strain) with ap-
proximately 4,()00 particles. The smoothing length was
0.127 cm. An dasctic-perfectly plastic constitutive
model and Gruneisen equation of state were used to
describe the solids. No explicit failure model was in-
cluded in the calculation. Figure 5a shows the alumin-
ium plate being impacted (t = 211_s). Figure 5b shows
the calculationat result at IS0 _ts. The projectile has
struck the first steel plate aqd the lower aluminum
plate which was set in motion by the impact has also
hit the steel and started to buckle. At 325 p.s, as shown
in Figure 5c, the aluminum plate has continued to
buckle and the portion of the broken steel plate at the
bottom of the figure has rotated as a result of the im-
pact torque. Jhese are two interesting features of the
strength model operating in the code. It is very en-
c_mraging to see these effects captured by the code.
Other interesting features are the crack t_rmation at
the back ofthe thick steel plate and the enhanced up-
ward momentum of the first steel plate due to the cra-
ter splash from the projectile on the second plate. We
expect these kinds of secondary effects to be impor-
tant in the actual satellite breakup from impact. An
obvious key feature of simulali(m is the "'plug'" of steel
plate seen in Figure 5d. This is not due to any explicit
failure model in the code but results from intrinsic
model fracture in SPH. In response to elastic waves
in the plate, some particles find themseb,'es outside of
the smoothing length range of communication with its
neighbors. This separation manifests itself as a
"crack" which propagates through the metal. We can-
not, at this point, claim that this effect is actually a
physical one. Nevertheless, it appears that the code is
trying, on its own, to accommodate failure, and the re-
suits seem physical. This calculation required 2
hours ofcpu time on the CRAY 2 at the Phillips l_abo-
ratory.
Results of a hypervelocity impact (7 kin/s) simulation
of an aluminum projectile into a water-filled alumi-
num tank are shown in Figure 6 where the particles are
gray-scaled according to their density. The diameter
of the tank was 25 cm initially and the wall thickness
was 0.5 cm. The projectile length was 3.0 cm and the
thickness was 2.0 cm. The geometry was 2D Carte-
sian. Approximately 20,00(} particles were used in the
simulation. The smoothing length was 0.2 cm. Notice
the shock propagation in the water and along the tank
inner surface which comes to a fi)cus at the rear of the
cylinder and then strongly reflects back. The reflected
shock is evidenced by the flattening of the particle dis-
tribution just ahead of the projectile. Notice also the
rapid deceleration of the aluminum projectile and its
large deformation. This calculation took 7 hours on
the CRAY 2. For these two specialized problems
there is no experiment data to which the simulations
can be compared, so we must be careful not to draw
unjustified conclusions about the codes performance.
However, we can get a feel for how the code responds
to difficult impact problems with the goal of extending
the calulations to three-dimensions with extensive
comparison to experiments.
CONCLUSIONS
The Smoothed Particle Hydrodynamics (SPH) ap-
proach to computational fluid dynamics has been
briefly described with emphasis on its natural ability
to model hypervelocity impact on orbiting structures.
Our goal is to exploit these virtues of SPtt towards the
development of a complete structural breakup model
in order to answer important questions concerning the
survivability of space assets due to kinetic impacts.
774
Q(4a) Initial configuration.
J
b- •
(4b) i0 i,_icroseconds after initial impact.
FigLIL_e 4. Material plot of a tantalum projectile penetrating an aluminurl _.
A-f[-ame stL-ucture at 60 ° obliquity.
775
!J
!
(4c) 20 microseconds after initial impact•
!
t
i
J
(4d) 30 microseconds after initial impact
Figure 4 (cont) Material plot of a tantalum projectile penetrating an
aluminum A-frame structure at 60 ° obliquity
776


Simulating hypervelocity impact effects on structures using the smoothed particle hydrodynamics code MAGI

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