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8th International Symposium on Interaction of the Effects of Munitions with Structures
22-25 April 1997, Virginia, USA
THE APPLICATION OF SPH TECHNIQUES IN AUTODYN-2DTM TO KINETIC
ENERGY PENETRATOR IMPACTS ON MULTI-LAYERED
SOIL AND CONCRETE TARGETS
Richard A. Clegg(1), Jim Sheridan(2), Colin J. Hayhurst(1), Nigel J. Francis(1)
(1) Century Dynamics Ltd, Dynamics House, Hurst Road, Horsham, West Sussex, RH12 2DT
(2) Defence Research Agency, Farnborough, Hants, GU14 6TD
ABSTRACT
Grid based Lagrangian and Eulerian techniques are often used for the numerical simulation of Kinetic Energy
Penetrator (KEP) impacts on soil and concrete targets. For this class of problem, an interesting alternative to these
traditional numerical techniques is Smooth Particle Hydrodynamics (SPH). Although SPH is not yet a mature
technology, it offers great promise; while maintaining all the potential advantages of a Lagrangian method (i.e.
efficient tracking of material interfaces and flexibility in terms of incorporating sophisticated material models) SPH
is a gridless technique and therefore removes the problem of grid tangling.
The results of a preliminary study carried out to assess the performance of SPH for the simulation of KEP attacks on
geological materials is presented here. An overview of the SPH capability implemented in the hydrocode
AUTODYN-2D is first given. SPH simulations of KEP impacts on soil and concrete targets are then described. The
simulation results were compared with Euler/Lagrange and Lagrange/Lagrange numerical simulations and also with
the results of field trials. The results indicate that SPH can contribute significantly to the capabilities and
performance of hydrocodes when applied to KEP attacks on geological materials.
INTRODUCTION
The Defence Evaluation and Research Agency (DERA), an executive agency of the UK Ministry of Defence, has a
history of research in hard target penetrating warhead concept design and terminal effectiveness assessment. The
study presented in this paper supports DERA’s Applied Research Programme on the development of air delivered
warheads for interdiction, strike and offensive counter air missions. Century Dynamics Limited (CDL) is a
specialist engineering and scientific software house and consultancy company providing software and consultancy
to DERA and other similar clients worldwide.
Hydrocode solution procedures and relevant material models have been evaluated and developed as part of this
programme. The coupled Euler/Lagrange technique within AUTODYN has generally provided the best predictions
of warhead penetration depth. It has also produced acceptable predictions of the transients measured by on-board
accelerometers in trial rounds. Relatively simple constitutive models based on static triaxial data for concrete and
soil are usually used for such simulations. However, whilst the response of the Lagrangian penetrator is well
characterised, the failure of the target is generally poorly represented by an Euler solution technique.
In grid based Lagrangian techniques, the sophisticated constitutive models which are required to represent the
critical areas of concrete structural behaviour; hydrostatic compaction, yielding, damage, cracking, and the effects
of reinforcement, can be included. However, the large deformations which are encountered local to the penetrator
lead to excessive grid distortions and tangling. Hence, to obtain a solution, analysts usually resort to using an
erosion algorithm. In this numerical technique energy is always removed from the system being analysed i.e. it is an
unphysical numerical process. In Eulerian techniques the problem of grid tangling does not arise. However, the
implementation of sophisticated constitutive models to properly account for the anisotropic behaviour of concrete
due to cracking and reinforcement is extremely difficult.
To investigate the possible benefits of alternative numerical techniques for this type of application, DERA and CDL
formed a partnership to research and develop a Smooth Particle Hydrodynamics (SPH) algorithm. SPH is a
relatively new numerical technique suitable for simulating KEP impacts on soil and concrete targets. Although SPH
is not yet a mature technology it offers great promise: SPH is a gridless Lagrangian technique, hence grid tangling
problems are precluded, and it is very flexible for incorporating sophisticated material models. CDL have to-date
incorporated the developed SPH algorithm within AUTODYN-2D.
An overview of SPH and the capability implemented in the hydrocode AUTODYN-2D is presented. One of the
motivations for the development of the SPH software was because of the natural way in which fracture and
fragmentation can be modelled. Such phenomena are characteristic of the response of geological materials,
including concrete, when subject to Kinetic or Chemical Energy weapons attack. As part of a validation and
performance assessment of the developed SPH capability, DERA asked CDL to undertake a blind prediction of two
trials it had undertaken using an instrumented 20kg tungsten penetrator. Both firings were at a nominal 520m/s
impact velocity; one was against a single 1m concrete layer, the other against 2m soil overlaying 1m of concrete.
Both qualitative and quantitative comparisons between observed and simulated target damage and KEP deceleration
are presented and discussed here.
AUTODYN OVERVIEW
AUTODYN-2D and 3D are fully integrated and interactive codes specifically designed for transient non-linear
dynamics problems [ 1]; such codes are commonly referred to as hydrocodes. AUTODYN-2D and 3D are
commercial hydrocodes which are in worldwide usage and are proprietary to Century Dynamics. They are
particularly suited to the modelling of impact, penetration, blast and explosion events [ 2]. Currently Lagrange,
Shell, ALE, Euler and Euler-FCT solution techniques are available in AUTODYN-2D and 3D, and these can be
coupled in several ways in space and time. The SPH capability described here has been developed initially for
AUTODYN-2D.
SPH - Motivation
The Lagrange processor, in which the numerical grid distorts with the material, has the advantage of being
computationally fast and gives good definition of material interfaces. The Euler processor, which uses a fixed grid
through which material flows, is computationally more expensive but is often better suited to modelling larger
deformations and fluid flow.
The ability of the Lagrangian (i.e. Lagrange and Shell) processors to simulate impact problems with large
deformations efficiently can be enhanced by the use of an erosion algorithm. The erosion algorithm works by
removing Lagrangian zones which have reached a user-specified strain, typically above 150%. In AUTODYN the
user can optionally choose to discard or retain the mass and momentum of nodes associated with discarded zones.
Although a very useful numerical technique for overcoming the problems of grid distortion, it is important to note
that erosion algorithms were not originally developed to model the physics of the problem.
SPH is a Lagrangian technique having the potential to be fast, accurate and efficient at modelling material interfaces
and flexible in terms of the inclusion of specific material models. In addition, SPH is a gridless technique so it does
not suffer from the normal problem associated with Lagrangian techniques of grid tangling in large deformation
problems. The fact that SPH is gridless also allows the modelling and visualisation of material fracture and
fragmentation to be dealt with in a more natural way.
It is acknowledged by the authors that SPH technology is relatively immature, compared with standard grid based
Lagrangian and Eulerian techniques, and several challenges remain before the technique can become a fully fledged
computational continuum dynamics technique. The known problem areas are stability, consistency and
conservation. The authors are currently investigating the implementation of the latest research in these areas [ 3], [
4] which purports to overcome these problems.
SPH - Basic Principles
Grid based methods, such as Lagrange and Euler, assume a connectivity between nodes to construct spatial
derivatives. SPH uses a kernel approximation, which is based on randomly distributed interpolation points with no
assumptions about which points are neighbours, to calculate values of functions and their derivatives.
The term “Particle” associated with the name SPH is appropriate for describing the Lagrangian motion of mass
points in SPH, however it is misleading because the “Particles” are really interpolation points. For example, the
density at particle I (Figure 1) can be calculated, using the kernel estimate, as
ρIJ
J
N
mW=
=
∑
1
IJ
In the above, the sum of the mass, mJ, of each neighbour particle (shown as shaded in Figure 1) multiplied by a
weighting function, WIJ, is taken over all particles within a specified radius of particle I. The radius is usually
defined as twice the smoothing length, h, if the cubic B-spline is used as the weighting function. The smoothing
length, in turn, defines the resolution length scale of the calculation. In this way the SPH particles act as sampling
(interpolation) points rather than interacting masses.
I
W
r
I-J3
r
I
2h
J1 J2 J3 J4
Density at I, ρI = mJ1WI-J1 + mJ2WI- J2 + mIWI-I
+ mJ3WI-J3 + mJ4 WI-J4
WI-J3
B-Spline Kernel
a) 2D Particle Neighbourhood b) Example 1D Density Calculation
Figure 1 The Kernel Approximation
Spatial derivatives of functions are calculated similarly by summing the values of the function multiplied by the
derivative of the kernel for each neighbouring particle.
AUTODYN-2D SPH - Basic Features
The SPH capability which has been fully integrated into the AUTODYN-2D software includes the same operational
features as for the standard grid based Lagrange processor. SPH problems can be run in axial or planar symmetry
and can include any of the equation of state, strength and failure material models standardly available within
AUTODYN. Other features include: A pre-processor which allows automatic packing of SPH particles into
arbitrary, user-defined geometries; explosive burn logic; a smoothing length which can vary in space and time
depending on the local changes in density; alternate forms of the SPH equations; an SPH impact/separation interface
for improved accuracy of initially separated impacts.
One additional feature of the SPH implementation in AUTODYN-2D is the ability to interact SPH nodes with
standard Lagrangian surfaces (Lagrange, ALE and Shell processors). This allows the user to model regions which
undergo small deformations using a traditional grid based Lagrangian processor while those regions experiencing
large deformation can be modelled using SPH. This allows flexibility and greater efficiency for solving some
problems that would otherwise have to be analysed using either one of the processor techniques in isolation.
AUTODYN-2D SPH - Verification and Validation
The functionality, accuracy and robustness of the current AUTODYN-2D SPH capability has been investigated
through a series of test cases. These range from one dimensional verification tests with known analytical solutions
to practical validation cases of real engineering problems, the problem of KEP impacts on soil and concrete targets
described here being one such validation example. Further details of validation work concerned with hypervelocity
and ballistic impact can be found in [ 5] and [ 6].
KEP SIMULATIONS
The problem of KEP impacts on soil and concrete targets has been an area of interest to the DERA and CDL for a
number of years. Traditionally such problems have been simulated numerically using Lagrange, Euler and coupled
Lagrange/Euler processor techniques, such as those in AUTODYN-2D and 3D. Such simulations have generally
resulted in reliable and accurate predictions of depth of penetration and/or residual velocity. However reproduction
of observed failure regions, in particular target front face spall, has been somewhat elusive. A study of the
performance of SPH for this type of problem has therefore been carried out to establish potential benefits over the
traditional grid based numerical techniques.
It is noted here that the accuracy of a numerical simulation depends on many factors in addition to the processor
technique. In particular, for impacts on brittle geological materials, a major factor is the suitability of the
constitutive relations and associated material input data being used. Whilst this is an area of very active research
within DERA and CDL, it is beyond the scope of this paper.
Field Trials
To assess traditional and SPH processor techniques for the simulation of KEP impacts on geological materials, a
suitable set of experimental data with which to compare the results was required.
The experimental data used to support this study was selected on the basis of it’s quality and completeness. The
objective of the selected trials was to investigate the application of tungsten alloys to hard target KEP warheads and
to develop instrumentation for on-board measurement and recording of deceleration transients through multi-layered
targets. The 20kg penetrators were fabricated from Ni, Fe, Co tungsten alloy, with a calibre of 90mm, an overall
length of 388mm, and having an ogive nose with calibre head radius (CHR) of 2.5.
The penetrators were fired from a 90mm smooth bore Howaster powder gun at a nominal speed of 520m/s. The 3m
diameter targets were produced by assembling a number of flanged cylindrical steel drum sections, as appropriate.
The concrete sections were precast at least 28 days prior to testing. The targets were then assembled on their sides,
as required for the trials, with the empty drums being filled with soil or sand through hatches in their uppermost
edge and allowed to settle for a few days. The soil was topped up immediately prior to testing.
The targets were set up in line with the gun launcher and instrumented to provide high speed photographic records
of the penetrators prior to impact and after exiting the final layer - mirrors being used to provide information on
projectile yaw. All impacts were normal to the target surface and on the target axis. Those shots which provided
good quality, consistent accelerometer transients are identified in Table 1. For the current SPH validation exercise,
only shots #5 and #11 were simulated.
Table 1 Trial Target Configurations
Shot Number Target Description Impact Velocity
5 1m Concrete 520 m/s
11 2m Soil + 1m Concrete 520 m/s
12 0.5m Concrete + 2m Soil + 0.5m Concrete 510 m/s
13 0.5m Soil + 0.5m Concrete + 1m Air + 0.35m Concrete 525 m/s
14 0.5m Soil + 0.5m Concrete + 0.5m Soil + 0.5m Concrete
+ 2m Air + 0.35m Concrete
520 m/s
a) Target Front Face b) Target Back Face
Figure 2 Shot #5 Target Damage Observed During Trials
Numerical Simulations
The SPH capability currently implemented in AUTODYN-2D was used to simulate the trial firings, shot #5 and
#11, described above. The simulations were carried out blind, the analysts carrying out the work having no prior
knowledge of the trial results. Simulations were also carried out using the traditional coupled Euler/Lagrange and
Lagrange/Lagrange processor techniques.
The KEP penetrator was modelled using the Lagrange processor in all simulations. The penetrator was observed to
undergo little or no deformation during the trial firings. A linear equation of state and elastic strength model was
used to represent the penetrator material.
The concrete (and soil for shot #11) materials in the target experience large deformation local to the penetrator, and
cracking occurs over large regions of the target. In the case of the SPH simulation, the targets were represented by a
uniform rectangular lattice of particles of 10mm diameter (smoothing length). In the case of the Euler targets
uniform cells of side 10mm were used in the impact region, the radial dimension of the cells was then gradually
graded to the outer radius of the target.
Interaction of the KEP with the SPH and Lagrange target was achieved using a master/slave contact algorithm while
for the Euler target the interaction was achieved via a polygon attached to the outer surface of the penetrator.
For the purpose of this work, the soil and concrete materials were represented using well established constitutive
relations which model the two major aspects of geological material behaviour under impact and blast type loading
conditions: Firstly, the volumetric compaction of the material under high pressure was modelled using a “Porous”
equation of state; secondly a pressure dependent yield surface was used to represent the shear response of the
material. In addition, a tensile hydrodynamic failure criteria was used to simulate tensile cracking in the materials.
In this model, cell failure is initiated when the tensile pressure exceeds a specified limit. On failure, the pressure,
deviatoric stresses and shear strength of the material are set to zero.
The input data for the hydrocode constitutive models was obtained from laboratory triaxial testing of the materials
used in the trial firings. The triaxial cell comprised an externally strain gauged 12.5mm thick steel cylinder, of
150mm length and 75mm internal diameter - greased and lined - into which concrete core samples were potted. The
end load was provided, to the test specimen only, by a 300 tonne Amsler test rig. The axial stress and strain
components were determined from the end platen load and displacement, whilst the radial stress and strain
components were calculated from the axial and hoop strains of the steel cylinder using elastic thick cylinder theory.
A single test can be used to completely characterise the specimen’s properties under compression - providing
pressure/density data for the porous equation of state and yield stress/pressure data for the shear failure surface. The
hydrodynamic tensile failure criteria was based on the indirect tensile strength determined using the Brazilian test
method [ 7].
It is recognised by the authors that more sophisticated constitutive models exist for geological materials which
include a more comprehensive representation of the material behaviour. For example; strain hardening/softening,
strain rate effects, strength differences in triaxial compression and extension, orthotropic tensile crack softening.
However these “state-of-the-art” models, and the material data input required for them, are not well established.
The basic models used here, with well established material data, are thus adequate for the purpose of this study to
assess the potential benefits of the SPH method.
It should be noted that the triaxial data used for this model was based on static plain strain loading. Current DERA
research directed at developing stress/strain/rate path dependent algorithms and associated experimental methods
will be reported in the near future.
RESULTS
Target Damage
The predicted deformation of the concrete target (shot #5) 3.5msecs after the impact of the KEP is shown in Figure
3 for the SPH/Lagrange, Euler/Lagrange and Lagrange/Lagrange numerical simulations. Regions which are failed in
tension are shown in dark, thus giving an indication of the extent of cracking in the concrete.
a) SPH/Lagrange
c) Lagrange/Lagrange
b)
Euler/Lagrange
Figure 3 Shot #5 Final Deformation, SPH/Euler/Lagrange Simulations
A qualitative comparison of the target damage predicted in the three numerical simulations indicates that the
SPH/Lagrange simulation gives rise to a much more discrete representation of the failed regions. Further, the size
and shape of the front face spall and back face scab are visualised particularly well. In SPH the separation of
material on a fracture plane, and the creation of new internal material interfaces, is dealt with in a natural way with
no prior knowledge required with respect to the crack location. Further, the opening of cracks can be seen as the
SPH particles separate. In grid based techniques the opening of cracks only manifests itself through the growth of
failed zones/material which can be much more difficult to observe.
In Table 2 an approximate quantitative comparison of the dimensions of the failed concrete regions indicates good
correlation with the trial. Similar damage characteristics can be marginally discerned from the results of the
Euler/Lagrange simulation however the correlation with the trial results is more difficult to define. In the
Lagrange/Lagrange simulation, although failed regions are concentrated near the KEP entry and exit points, no
discrete crack patterns can be observed or correlated with the trial.
Table 2 Shot #5, Comparison of Trial and Predicted Target Damage
Shot #5 Target Damage Observed Trial Predicted Damage (mm)
Diameters Damage (mm) Euler/Lag SPH/Lag
Bore Hole 90 (±10) 90 (±10) 90 (±10)
Primary Front Face Spall 1500 (±150) 2000 (+1000) 1200 (±100)
Back Face Spall 2200 (±200) 2380 (+620) 1900 (±200)
The predicted deformation of the soil and concrete target (shot #11) after penetration of the KEP is shown in Figure
4 for the SPH/Lagrange numerical simulation. Regions which are failed in tension are shown in dark, thus giving an
indication of the extent of cracking in the concrete. Again a discrete representation of the cracking in the concrete is
observed.
Figure 4 Shot #11, SPH/Lagrange Target Damage
KEP Deceleration
In the trial, the deceleration of the KEP was measured via an onboard accelerometer. For comparison, the average
deceleration of the KEP was recorded in each of the numerical simulations. These are compared in Figure 5 and
Figure 6 for shots #5 and #11 respectively.
-250000
-200000
-150000
-100000
-50000
0
50000
100000
00.2 0.4 0.6 0.8 11.2
Penetration (m)
Accln
(m/s/s)
SPH/Lagrange
Lagrange/Lagrange
Euler/Lagrange
Trial
CONCRETE
Figure 5 Shot #5 KEP Deceleration
0.5 11.5 22.5 3
Penetration (m)
SPH/Lagrange
Euler/Lagrange
Accln
(m/s/s)
Trail
SOIL CONCRETE
Figure 6 Shot #11 KEP Deceleration
-250000
-200000
-150000
-100000
-50000
0
50000
100000
0
The general characteristic features of the KEP deceleration for the two target configurations and the three processor
techniques show good correlation with those observed in the trial. For the soil and concrete target the timing and
sharp rise in deceleration of the KEP at the soil/concrete interface is well represented (Figure 6). For both target
configurations the average peak deceleration is however under-predicted by 20% to 30%. Further, the under
prediction of the peak deceleration is greater for the SPH target compared with the Lagrange and Euler targets. It
should be noted that the spike in the trial KEP deceleration time history at approximately 0.25m penetration (Figure
5) is thought due to be a characteristic of the accelerometer rather than physical phenomena.
At the time of analysis, it was known to the authors that certain improvements could be made to the SPH algorithms
used in these simulations. In particular, the performance of SPH in tension could be improved using the methods
presented in [ 3] and [ 4]. Inclusion of these or similar algorithms may lead to improved correlation of the
SPH/Lagrange simulations with the trials as the penetrator approaches the back face of the target.
The general trend to under predict the maximum deceleration of the KEP could be due to many factors including the
processor techniques being used. However, one major factor is the appropriateness of the constitutive models used
to represent the materials in the above simulations. Under the loading conditions experienced, soil and concrete
materials are known to exhibit complex highly non-linear behaviour. Enhancements to the constitutive models used
here to include effects such as strain hardening and softening, strain rate hardening, time dependent crack growth
and anisotropic post-crack strength would most probably result in improved correlation between the predicted peak
decelerations and those observed in the trial. It should be noted however that the introduction of more complex
constitutive models requires more sophisticated material testing to obtain appropriate data input. This is an area of
research that is being actively pursued by DERA and CDL.
CONCLUSIONS
This paper presents a study which has been carried out to assess the performance of SPH numerical techniques for
the simulation of KEP attacks on geological materials. It is shown that the SPH technique implemented in
AUTODYN-2D is well suited to predicting the response of geological materials under KEP attack. In particular, the
size and shape of both front and back face target fracture regions can be visualised particularly well and good
correlation with trial observations is obtained. Further, observed field trial KEP deceleration characteristics can be
predicted using SPH with a level of accuracy comparable to traditional grid based Eulerian and Lagrangian
numerical techniques, although the general trend is to under-predict the average peak deceleration by up to 30% in
the simulations presented. The use of more sophisticated constitutive models, and associated material input data,
than those used in this initial work is likely to improve such correlations.
Although still relatively immature the SPH technique shows great promise for the numerical simulation of KEP
attacks on hardened structures. Further SPH development and application work is underway including an extension
of this work to 3D.
REFERENCES
[ 1] Birnbaum NK, Cowler MS, “ Numerical Simulation of Impact Phenomena in an Interactive Computing Environment”,
Proc. Of Int. Conf. On Impact Loading and Dynamic Behaviour of Materials, “IMPACT ’87”, Bremen, Germany, May
1987.
[ 2] Robertson NJ, Hayhurst CJ, Fairlie GE, “Numerical Simulation of Impact & Fast Transient Phenomena Using
AUTODYN-2D and 3D”, 12th Int. Conf. On Structural Mechanics in Reactor Technology IMPACT IV Seminar, Berlin,
Germany, August 1993.
[ 3] Randles PW, Libersky LD, "Smooth Particle Hydrodynamics: Some Recent Improvements and Applications", Computer
Methods in Applied Mechanics and Engineering, Meshless Methods, 1996, preprint.
[ 4] Randles PW, Libersky LD, Carney TC, "An Improved Method for Determining the Resolution Scale in SPH and its
Effects on the Impact Fracture of Steel Cubes", 16th Int. Ballistics Symposium and Exhibition, "Ballistics '96", San
Francisco, California, USA, September 1996.
[ 5] Hayhurst CJ, Clegg RA, "Cylindrically Symmetric SPH Simulations of Hypervelocity Impacts on Thin Plates", Int. J.
Impact Engng. (to be published), Hypervelocity Impact Symposium, Freiburg, Germany, October 1996.
[ 6] Hayhurst CJ, Clegg RA, Livingstone IH, Francis NJ, "The Application of SPH Techniques in AUTODYN-2D to Ballistic
Impact Problems", 16th Int. Ballistics Symposium and Exhibition, Ballistics '96, San Francisco, California, USA,
September 1996.
[ 7] Sheridan AJ, Pullen AD, Newman JB, "The Search for a General Geological Material Model for Application to Finite
Element Methods and Hydrocodes", Structures Under Shock and Impact II, June, 1992.
