1

American Institute of Aeronautics and Astronautics 092408

Explosion Damage Prediction of Advanced Space

Structures Subject to Hypervelocity Impact

M. Dal Santo1, J. Bayandor

2

School of Aerospace, Mechanical and Manufacturing Engineering

Royal Melbourne Institute of Technology

Melbourne, VIC, 3001, Australia

Advanced space structures such as satellites and spacecraft, particularly in Low

Earth Orbit, are at risk of collision with man-made space debris and micrometeorites.

Such collisions occur at hypervelocity and are capable of causing potentially catastrophic

damage in the event of an impact. In order to capture this extreme and explosive

phenomena, discretised techniques were proposed and applied, including a meshless

Lagrangian Particle Method which can be tailored for high deformation behavior. Such

violent impact scenarios are heavily time dependant, hence requiring the use of time

marching explicit schemes to analyze the problem over discretised intervals. This paper

reports on simulations which have been conducted with regards to both metallic and

composite protective shielding.

Nomenclature

A, B = strain rate hardening parameters [N.m-2

]

C = strain hardening coefficient [1]

c0-3 = material constants [N.m-2

]

c4-6 = material constants [1]

e = specific internal energy [J.kg-1

]

εp = equivalent plastic strain [1]

εp = equivalent stain rate [1]

h = smoothing length [1]

m = thermal softening power exponent [1]

n = strain hardening power exponent [1]

ρ = density [kg.m-3

]

ρ 0 = initial density [kg.m-3

]

Ux

= velocity components [m.s-1

]

xß

= spatial components [m]

T*

= normalized temperature [K]

Troom = room temperature [K]

Tmelt = melting temperature [K]

σ = equivalent stress response [N.m-2

]

σp = effective plastic stress [N.m-2

]

σxβ

= stress tensor [N.m-2

]

I. Introduction

In the last several decades of space exploration, there has been a significant increase in the number of man-

made space debris especially in Low Earth Orbit (LEO: 200-2000 km), which represent a significant danger to

the safety and operational efficiency of spacecraft and satellites. Debris orbiting the Earth at velocities of several

kilometers per second are capable of colliding with space vehicles. Such collisions can be referred to as

1 Final Year Undergraduate Student, AIAA Student Member

2 Thesis Supervisor, AIAA Senior Member

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposi4 - 7 January 2010, Orlando, Florida

AIAA 2010-73

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

2

American Institute of Aeronautics and Astronautics 092408

Hypervelocity Impact (HVI), which may cause significant or potentially catastrophic damage to space

structures. Figure 1, depicts the higher density of space debris found in LEO, which increases the risk of HVI

occurring.

Such violent encounters can result in undesirable damage to spacecraft components and unacceptable loss

of life for manned missions. In order to avoid such catastrophic events the need to develop adequate shielding

has become apparent. To ensure the designs of space structures are capable of withstanding HVI a significant

amount of experimental testing is required. Experimental trials can utilize facilities such as Light Gas Guns

which can achieve projectile speeds in the order of several kilometers per second. This is an expensive

procedure that may be well complimented with the introduction of a numerical analysis tool to analyze a wider

range of impact scenarios, including speeds which may not be experimentally achievable, with drastically lower

costs.

Figure 1. Spatial density vs. altitude for objects larger than 1 mm diameter

1

This paper investigates the mechanics involved in HVI and outlines a methodology based on which a

numerical analysis has been constructed. Simulations have been performed to analyze and compare the behavior

of both metallic and composite space structures under HVI conditions. Due to the highly time dependant nature

of such events, explicit Finite Element (FE) schemes need to be utilized to analyze the problem over discretised

intervals. Simulations have been conducted within the Pam-Crash suite of software which incorporates an

explicit FE solver.

II. Shielding

HVI is a powerful and complex phenomenon involving many simultaneous interactions occurring over a

very short time period. When an impact occurs at hypervelocity large temperatures, pressures and shock waves

are generated which rip through the structure and in the case of metals, cause the material to behave in a

hydrodynamic fashion. When the structure is penetrated, a multiple phase debris cloud is formed consisting of

fragments from both the perforated surface and the impactor, generating plasma in the process. Fragmented

material can exist in combinations of solid, molten and vaporized states, forming a multiple phase debris cloud.

Challenges exist in designing spacecraft shields which can both withstand and contain HVI, whilst providing

sufficiently light structures.

As depicted in Fig. 2, space structures designed to shield against HVI typically consist of a series of thin

bumper shields to progressively absorb energy from the impact. In triple bumper shielding systems the function

of the initial plate is to fragment and vaporize the impactor as much as possible in order to distribute the debris

over a wide region. Secondary plate is designed to defeat these fragments and further reduce the velocity of the

remaining material. Rear wall is generally the thickest part of the shield and is designed to absorb momentum

and resist fracture thus shielding the inner structure.

Figure 2. Triple bumper shielding

2

3

American Institute of Aeronautics and Astronautics 092408

Experimental studies have shown the benefits of implementing composite materials in secondary plates in

order to provide a lighter structure than the more traditional triple shield aluminum design. For instance,

replacing an aluminum secondary bumper with an aramid-epoxy design delivers mass savings and further

improves damage tolerance.3 Simulations conducted in this paper aim to demonstrate some of these capabilities

in aluminum and aluminum/composite shielding systems.

III. Smoothed Particle Hydrodynamics

In order to capture the extreme and explosive phenomena encountered in HVI, several numerical modeling

techniques were considered including Lagrangian and Eulerian methods. Eulerian techniques were not selected

due to the occurrence of mesh warping/entanglement under high deformations, and the consequently high

computational time required.4 Lagrangian Particle Methods however, were unique in the sense that they were

not constrained by any type of mesh, thus offering tremendous advantages in simulating high strain behavior.

Therefore a Lagrangian Particle Method known as Smoothed Particle Hydrodynamics (SPH) was selected for

modeling HVI. In SPH particles each have their own sphere of influence which enables them to interact with

each other.

An SPH particle consists of a centre of mass, a particle radius r and a smoothing length h which is shown in

Fig. 3 below. The strength of a particle‟s influence is governed by a smoothing function and the range of its

influence is controlled by the smoothing length parameter, with the influence strength reaching zero at a

distance of 2h from the centre.

Figure 3. SPH particle representation

5

In order to govern the strength of interaction between particles it is necessary to implement a suitable type

of Kernel function.

A. Kernal Approximation

Consider the following function f in Eq. (1) where 𝛿 is the delta function;

< 𝑓 𝑥 > = 𝛿 𝑥 − 𝑥 ′, ℎ 𝑓 𝑥 ′ 𝑑 𝑥 ′

𝛿 𝑥 − 𝑥 ′, ℎ 𝑑𝑥 ′ = 1∞

−∞ (1)

Equation 1 states that the value of a point in a continuous function can be extracted from its integral by

using a delta function 𝛿 as a filter.6

Delta function can be replaced by Kernel function W, which has a fixed domain measured by the smoothing

length parameter h but still obeys the basic delta function properties.

limℎ→0 𝑊 𝑥 − 𝑥 ′, ℎ = 𝛿 𝑥 − 𝑥 ′ (2)

Introducing this Kernel function into Eq. (1) yields the following equation:

< 𝑓 𝑥 > = 𝑊 𝑥 − 𝑥 ′, ℎ 𝑓 𝑥 ′ 𝑑 𝑥 ′ (3)

Kernel function is now able to extract the value from any point across a continuous function.

4

American Institute of Aeronautics and Astronautics 092408

B. Particle Approximation

Up to this point the definition of the proposed smoothing kernel has addressed continuous functions, which

is not applicable to a series of discreet SPH particles. In order to ensure compatibility with SPH formulation, the

integral in Eq. (3) was modified through use of the Particle Approximation, which discretised the domain so that

it is no longer continuous. Equation (3) can be evaluated by a summation over a series of discreet points as

depicted in Eq. (4).

< 𝑓 𝑥 > ≅ 𝑓𝑗 𝑊 𝑥 − 𝑥 ′, ℎ 𝑚 𝑗

𝜌(𝑥𝑗 )

𝑁𝑗=1 (4)

A volume has been associated to particle j:

𝑑𝑥 ′ =𝑚 𝑗

𝜌(𝑥𝑗 ) (5)

At any given point, the inter-particular force which exists is equal to the summation of the Kernel functions

imposed by the neighboring particles. The effect of Eq. (4) can be visualized in Fig. 4, where the overlapping of

Kernel functions are summed at a particular point known as „smoothing‟, hence the name „Smoothed Particle

Hydrodynamics‟.

Figure 4. Particle interaction (only 3 shown for clarity) 7

Kernel function itself appears like a normal distribution and can be selected from a variety of functions. For

all simulations conducted in this study the W4 B-spline Kernel was selected, as seen in Fig. 5 below.

Figure 5. W4 B-spline Kernel

The W4 B-spline Kernel can be expressed mathematically as seen in Eq. (6).

𝑊4 𝑣, ℎ =

15

7

2

3− 𝑣2 +

1

2𝑣3 0 < 𝑣 < 1

5

14 2 − 𝑣 3 1 < 𝑣 < 2

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(6)

Where 𝑣 represents the normalized coefficients.

𝑣 = 𝑥𝑖 − 𝑥𝑗 ℎ (7)

Comparative studies which have been conducted suggest the smoothing length parameter should be left as

variable to obtain a more realistic representation of HVI behaviour.8

This can allow for the solver to adjust the

smoothing length depending upon particle spacing, particularly when a widely distributed debris cloud is

formed.

5

American Institute of Aeronautics and Astronautics 092408

C. Derivation of the SPH equations

Particle behavior is based upon the conservation laws of fluid dynamics.9 These laws once discretised

through use of the particle method, can be seen in Eq. 8, where i represents a given particle and j the

neighboring particles.

𝑑𝜌𝑖

𝑑𝑡= 𝜌𝑖

𝑚 𝑗

𝜌𝑗 𝑈𝑖

𝛽− 𝑈𝑗

𝛽 𝑗 𝑊𝑖𝑗 ,𝛽

𝑑𝑈𝑖

𝛼

𝑑𝑡= − 𝑚𝑗

𝜎𝑖𝑥𝛽

𝜌𝑖2 +

𝜎𝑗𝑥𝛽

𝜌𝑗2 𝑗 𝑊𝑖𝑗 ,𝛽

𝑑𝐸𝑖

𝑑𝑡=

𝜎𝑖𝑥𝛽

𝜌𝑖2 𝑚𝑗 𝑈𝑖

𝑥 − 𝑈𝑗𝛽 𝑗 𝑊𝑖𝑗 ,𝛽 (8)

Equations (8) were found to yield large unphysical oscillations near shockwaves because dissipative terms

have not been accounted for. With particles travelling at high velocities and possessing small surface areas, each

particle creates unrealistically high impact pressure and shockwaves. An artificial viscosity term represented by

𝛱, was implemented to smear the shockwave between particles as opposed to treating them individually.10

Although the viscous pressure is „artificial‟, it is a critical parameter which contributes towards producing

realistic shock behavior. Artificial heat conduction terms Hi have also been included to account for cases of

spurious heating.11

Equations (9) with the artificial viscosity and artificial heat conduction terms included are:

𝑑𝜌𝑖

𝑑𝑡= 𝜌𝑖

𝑚 𝑗

𝜌𝑗 𝑈𝑖

𝛽− 𝑈𝑗

𝛽 𝑗 𝑊𝑖𝑗 ,𝛽

𝑑𝑈𝑖𝛼

𝑑𝑡= − 𝑚𝑗

𝜎𝑖𝑥𝛽

𝜌𝑖2 +

𝜎𝑗𝑥𝛽

𝜌𝑗2 + Πij 𝑗 𝑊𝑖𝑗 ,𝛽 + 𝐻𝑖

𝑑𝐸𝑖

𝑑𝑡= 𝑚𝑗 𝑈𝑖

𝛼 − 𝑈𝑗𝛼

𝜎𝑖𝑥𝛽

𝜌𝑖2 +

1

2Πij 𝑗 𝑊𝑖𝑗 ,𝛽 + 𝐻𝑖 (9)

D. Equation of State

HVI encompasses many different aspects of physics during the impact. Extreme temperatures and pressures

generated during HVI constitute the large transfer of energy which occurs. Such violent impact causes the

material to deform significantly and to undergo phase changes to produce debris consisting of solid, molten and

vaporized states of matter, drastically effecting the material response. Solid material model selected to be used

for the impactor was Isotropic Elastic/Plastic Hydrodynamic, which can allow for severe phase change

according to the Polynomial Equation of State (EOS), defined in Eq. (10).

ecccccccP 2

654

3

3

2

210

𝜇 =𝜌

𝜌0− 1

(10)

Polynomial EOS is applicable only to solid element formulations which cater for SPH particles, but not the

shell elements in the target structure.

F. Strain Rate Law

HVI often results in both impactor and target fragmenting at very high velocities. This immediate

deformation occurs at high strain rates and is sufficient to generate large shock waves through metals. Strain rate

behavior is an essential part of HVI phenomenon. Strain rate law effects how metallic material will respond

during the impact including shock wave propagation, thermal effects, rupturing of the plate and the

corresponding formation of the debris cloud. This can take place through identifying and addressing the new

stiffness and material properties at the impact. Johnson-Cook‟s strain rate law was selected for its effectiveness

and simplicity and appears in the general form12

given by Eq. (11).

𝜎 = 𝐴 + 𝐵휀𝑝𝑛 1 + 𝐶 ln

휀 𝑝

휀 0 1 − 𝑇∗ 𝑚

𝑇∗ =𝑇 − 𝑇𝑟𝑜𝑜𝑚

𝑇𝑚𝑒𝑙𝑡 − 𝑇𝑟𝑜𝑜𝑚

(11)

6

American Institute of Aeronautics and Astronautics 092408

This law effectively accounts for high stress response of metallic materials with an increasing strain rate to

allow for behavior, otherwise not observed in the very structure while in pure solid state. Application is limited

to the target plates due to the shell formulation selected, though it is not applicable to SPH elements.

IV. Numerical Studies

Two numerical simulations have been presented and discussed in this chapter. Simulations have been

conducted to in order to demonstrate the characteristics of HVI onto spacecraft protection systems. Both impact

scenarios consist of a single projectile travelling at hypervelocity speeds and impacting a multi-layer shielding

system. Previously mentioned benefits of SPH include the ability to handle high strain problems with

comparative ease and efficiency. For this reason SPH particles will be used exclusively to model the high

velocity projectile which will impact the protective shielding. First numerical study consists of HVI onto a triple

layer protective shield, of aluminum construction. The second study will feature HVI onto a double bumper

shield with an initial aluminum protective layer followed by a fiber reinforced composite layer.

A. Metallic Shielding

1. Experimental Conditions

The following conditions were derived from testing conducted on a NASA B505 aluminum whipple shield.

These were used by Groenenboom8 who conducted a Two Dimensional (2D) SPH simulation and compared it

against a Eulerian Hydrocode simulation performed by Cykowski.13

Very good agreement was observed with

the Eulerian Hydrocode and on this basis the simulation was chosen for comparison. The HVI involves an

aluminum sphere impacting a „stuffed whipple shield‟, with a front bumper made from 6061-T6 aluminum and a

rear bumper made from 2219 aluminum. The „stuffing‟ consisted of 4 layers of Nextel AF62 and 4 layers of

Kevlar 710. However, both Cykowski and Groenenboom replaced these 8 layers of stuffing with a single sheet

of 1.947 mm thick aluminum panel for comparative purposes. This modification was retained for the simulations

conducted in the present work depicted in Table 1 below.

Table 1. Simulation Data

Experimental

Velocity

Impactor shape and

size Target panel thickness

Target panel

material

6.78 km/s @

60⁰ Al Sphere, 9.5 mm

First plate, 1.12 mm

Second plate, 1.95 mm

Third plate, 3.18 mm

Al 6061-T3

Al 2024-T3

Al 2219

2. Model Setup

As depicted in Fig. 6, the aluminum impactor was modeled with solid elements before being converted to

SPH particles. This rather dense sphere of particles was unconstrained by a fixed mesh allowing for large strains

and deformations. Particle interaction was controlled through a smoothing kernel in the form of the W4 B-spline

and a Polynomial EOS was applied to the SPH particles in order to capture multiple phase material behavior

experienced during HVI.

Figure 6. Solid FE and SPH impactor consisting of 11,488 particles

The target structure constructed as depicted in Fig. 7, consists of three aluminum plates modeled using shell

elements with the formulation „Elastic/Plastic deformation with Elastic Stiffening and Failure‟ applied. This

formulation allowed the plate to be perforated once elements have been damaged according to maximum strain

criteria, without which the elements would stretch to unrealistic proportions. In order to account for accelerated

7

American Institute of Aeronautics and Astronautics 092408

rupturing and high strain response unique to HVI , Johnson-Cook‟s strain rate law was adopted. Simulation was

conducted on an explicit solver which was most suitable in describing the highly time dependant behavior of

such a violent impact.

Figure 7. SPH impactor (black) triple shielding (shell elements)

3. Simulation

Simulation results in Fig. 8 show the significant deformation achieved by the aluminum impactor upon

impact with the majority of the material successfully penetrating the aluminum bumper shields. Initial impact

with the first plate resulted in severe fragmentation of the material which has both penetrated the shield and

reflected off the surface. It was observed that the oblique angle of impact led to the asymmetric behavior of the

debris cloud. More significant damage was caused to the secondary shield as the debris cloud was expanded,

thus creating a larger impact diameter than the original 9.5 mm sphere. Penetration of the secondary plate further

fragmented the projectile and reflected a large amount of particles back up to the first plate, though this was

unable to prevent failure of the third plate.

2 μs 45 μs 65 μs 90 μs 115 μs

Figure 8. Oblique HVI to triple shield

Figure 9 depicts a direct comparison of results obtained through this study with those obtained by the

Groenenboom 2D simulation. The results displayed similar material behavior, particularly with regards to

penetration of the target plates. Both simulations depicted the fragmentation of the impactor, producing an

expanding debris cloud which results in larger penetrations in the second and third plate, respectively. More

ejecta were reflected by the target plate compared to the Groenenboom simulation. However, a larger number of

particles were used to represent the impactor in the present study.

Figure 9. Comparison with Groenenboom simulation at 20 and 28 µs

8

American Institute of Aeronautics and Astronautics 092408

The impactor was fragmented immediately upon impact, although it retained the bulk of the material

travelling in the original direction. Impactor and corresponding debris cloud clearly penetrated the triple shield

as seen in Fig. 10, demonstrating the explosive nature of HVI. In the case of the triple bumper shield, the

aluminum material was significantly deformed and unable to absorb the impact. Though this preliminary

investigation, it can be seen that introducing a composite material as a secondary bumper shield can improve the

damage tolerance and has the potential to achieve an equivalent result with a lower structural mass than the

configuration examined in this study.

Figure 10. Damage to triple shield

Results achieved from this simulation further demonstrate the advantages of implementing meshless

techniques to model projectile behavior under high deformation conditions. The results achieved correlate well

with the simulation performed by Groenenboom and the general behavior observed during the impact.

B. Composite Shielding

1. Experimental Conditions

Riedel conducted a series of HVI experiments to test the space debris protection shield with reference to the

International Space Station (ISS) Columbus module.14

The following conditions outlined in Table 2 were used

in a simulation conducted by Riedel, which corresponded to the experimental test 4354. Unlike the previous

aluminum triple shielding case, this scenario specified in Table 2 incorporated an aramid-epoxy composite as

the secondary shield, with the intention of demonstrating the improvements in ballistic performance. Riedel

observed that for this particular experiment, „some of the composite layers were completely destroyed with no

clear hole produced‟.

Table 2. Experimental conditions for test 4354

Experiment velocity Impactor shape and

size Target panel thickness Target panel material

4.75 km/s Al Sphere, 7.0 mm First plate, 2.0 mm

Second plate, 5.7 mm

Al 6061-T6

Aramid-Epoxy

2. Model Setup

The previous impactor in Fig. 6 was retained as were the applied settings for this simulation. This includes

implementation of SPH particles and the Polynomial EOS however, the impactor size has now been reduced to

7.0 mm in diameter. The model created for this study is shown in Fig. 11, with the primary and second shields

separated by a distance of 150 mm. In a similar fashion to the previous modeling study, initial aluminium

shielding consists of shell elements with the formulation, „Elastic/Plastic deformation with Elastic Stiffening

and Failure‟ and Johnson-Cook‟s strain rate law implemented. Secondary layer however required a more

complex material model in order to describe the anisotropic properties of a fiber reinforced composite. A

multiple layer shell material model was applied which consisted of 18 layers of woven aramid fabric. Fibers

were orientated at angles of 0 and 90 degrees with the matrix consisting of a 38% epoxy resin volume fraction.

In a similar fashion to the metallic model used, composite shell elements were deleted once exceeding

maximum strain criteria.

9

American Institute of Aeronautics and Astronautics 092408

Figure 11. SPH impactor (a) metallic shield (b) composite shield (c)

3. Simulation

Figure 12 depicts the shockwave behavior of the initial metallic plate upon impact. With Johnson-Cook‟s

strain rate law enabled, shockwaves caused by the impact were observed expanding through the metallic

structure. With this law implemented, more realistic material failure and debris cloud formation were achieved,

thus improving the impact loading onto the composite portion of the shield.

7 μs 10 μs 18 μs

Figure 12. Shockwave behaviour captured by Johnson-Cook’s model

As seen in Fig. 13, the Polynomial EOS applied to the impactor facilitates the immediate fragmentation and

expansion of particles upon impact with the initial metallic plate, thus forming a multiple phase debris cloud.

The cloud then impacts the second plate while still travelling at hypervelocity speeds. Particles constituting the

debris cloud did not have sufficient impact energy to exceed the ballistic limit of the composite shielding and

therefore, could not penetrate the surface. A significant amount of impactor material was reflected back from the

initial aluminum target plate, due to the large amount of particles used.

8.3 μs 20 μs 35 μs 48 μs

Figure 13. HVI onto a doubly shielded space stuctural model

According to the experimental observations, „some of the composite layers were completely destroyed with

no clear hole produced‟.14

As depicted in Fig. 14, closer inspection of the composite panel revealed a small 20

mm perforation. In the simulation conducted, elements were removed due to exceeding their maximum strain

10

American Institute of Aeronautics and Astronautics 092408

criteria. Although this suggests the elements were severely damaged, no particles could penetrate the shielding

at any stage of the simulation. Therefore, the visual element deletion which occurred in post-processing was

considered to be premature, meaning the second plate was successful in shielding the space structure considered.

This simulation re-affirmed the ability of the composite material model to absorb the impact of the debris cloud

as observed in the experimental testing.

Figure 14. Element deletion in composite shield

V. Conclusion

Simulations presented in this paper clearly demonstrated the suitability of utilizing advanced meshless

Lagrangian Particle Methods to model high strain behavior exhibited during Hypervelocity Impact. The

inherent robustness of the Smoothed Particle Hydrodynamics formulation allows it to capture the debris

cloud formations which would be difficult to show using meshed based techniques.

In the case of the triple bumper shield of aluminum construction, results obtained compared well to the

referenced simulation particularly with regards to debris formation and material. Results obtained for the

Riedel experiment, while not perfect, demonstrated the capability of the composite material model

implemented to absorb impact from the hypervelocity explosion and resulting multiphase debris cloud.

Further study of the composite material model may lead to prevention of premature element deletion,

though general performance of the composite model agreed with experimental observations.

Research conducted in this study has established a working methodology from which numerical

analysis can be conducted. Applicability has been demonstrated on multiple layered shielding, which can

represent the protective shielding featured in spacecraft structures. Further development of the techniques

outlined in this study can facilitate creation of a numerical design and certification tool. Such analytical

capabilities would reduce the dependence on expensive experimental testing, thus contributing towards

designing lighter and safer space structures.

Acknowledgements

Discussions conducted with Prof. Bayandor‟s Dynamic Modeling Research Team, in particular with

Prof. J. Bayandor and Mr. A. Litchfield are acknowledged and much appreciated.

References

1Technical Report on Space Debris, Text of the Report adopted by the Scientific and Technical Subcommitte of the

United Nations. (A/AC. 105/720), 1999. 2Gorman MR, Ziola SM, Hypervelocity Impact (HVI) Volume 1: General Introduction. NASA/CR-2007-

214885/VOL1, 2007. Accessed online 10/9/2008. 3Destefanis R, Faraud M,. Testing of Advanced Materials for High Resistance Debris Shielding, International

Journal of Impact Engineering; 20:209-222, 1997. 4 Lichfield, A. and Bayandor, J. “Modelling of Explosion Damage Tolerance in Advanced Space Structures Subject

to Hypervelocity Impact in Microgravity”, Book of Abstracts: The 22nd Congress of the International Union of

Theoretical and Applied Mechanics, ISBN 978-0-9805142-0-9, Adelaide, South Australia, August 25-29, 2008. 5ESI Group, PAM-CRASH Solver Reference Manual, 2004 6Kamoulakos A, Groenenboom P. Moving from FE to SPH for space debris impact simulations – experience with

Pam-Shock, Proceedings of European Conference on Spacecraft Structures: Materials and Mechanical Testing,

Braunschweig, Germany, 1998.

11

American Institute of Aeronautics and Astronautics 092408

7Lichfield A. Modelling of Explosion Damage Tolerance in Advanced Space Structures Subject to Hypervelocity

Impact in Microgravity, BEng thesis, Royal Melbourne Institute of Technology, 2007. 8Groenenboom, P. H.L, Numerical simulation of 2D and 3D hypervelocity impact using the SPH option in PAM-

SHOCK, International Journal of Impact Engineering; 20:309-323, 1997. 9Libersky LD, Petschek AG, Theodore CC, Hipp JR and Allahdadi FA. High strain lagrangian hydrodynamics, a

three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109:67-75, 1993. 10Monaghan JJ, Gingold RA. Shock simulation by the Particle method. Journal of Computational Physics; 52:374-

389, 1983. 11Noh WF. Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux. Journal of

Computational Physics; 72, 1978. 12Milani AS, Dabboussi W, Nemes JA, Abeyaratne RC. An improved multi-objective identification of Johnson–

Cook material parameters, International Journal of Impact Engineering, doi:10.1016/j.ijimpeng.2008.02.003, 2003. 13Cykowski, E. Hydrocode modeling of stuffed whipple shields, LESC 31597, 1995. 14Riedel W, Nahme H, White DM, Clegg RA. Hypervelocity impact damage prediction in composites: Part II –

experimental investigations and simulations, International Journal of Impact Engineering; 33:670-680, 2006.