BIRD1

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International Journal of Impact Engineering 32 (2006) 1127–1144

0734-743X/$ -

doi:10.1016/j.

�CorresponUniversity o

+47 73 50 47 0

E-mail add

www.elsevier.com/locate/ijimpeng

A numerical model for bird strike of aluminium foam-basedsandwich panels

A.G. Hanssena,b,�, Y. Girardc, L. Olovssond, T. Berstadb, M. Langsetha

aStructural Impact Laboratory (SIMLab), Department of Structural Engineering, Norwegian University of Science and

Technology (NTNU), N-7491 Trondheim, NorwaybSINTEF Materials Technology, Rich. Birkelandsvei 2B, N-7465 Trondheim, Norway

cEADS CCR, quai Marcel Dassault – BP 76-92152 Suresnes Cedex, FrancedLSTC, 7374 Las Positas Road, Livermore, CA 94550, USA

Received 15 March 2004; accepted 9 September 2004

Available online 30 December 2004

Abstract

Experimental bird-strike tests have been carried out on double sandwich panels made from AlSi7Mg0.5aluminium foam core and aluminium AA2024 T3 cover plates. The bird-strike velocity varied from 140 to 190m/s. The test specimens were instrumented with strain gauges in the impacted area to measure the local strains of therear sandwich plate. A numerical model of this problem has been developed with the non-linear, finite elementprogram LS-DYNA. A continuum damage-mechanics-based constitutive model was used to describe thebehaviour and failure of the aluminium cover plates. The foam core was modelled by a pressure sensitiveconstitutive model coupled by a failure criterion on maximum volumetric strains. The bird was represented by anidealised geometry and the material model was defined by a linear equation-of-state. A multi-material arbitraryLagrangian Eulerian (ALE) element formulation was used to represent the motion of the bird, whereas thesandwich panel was described by a Lagrangian reference configuration. A fluid–structure interface ensured propercoupling between the motion of the bird and the solid materials of the sandwich panel. It was found that themodel was able to represent failure of both the aluminium cover plates as well as the aluminium foam core.r 2004 Elsevier Ltd. All rights reserved.

Keywords: Bird-strike; Aluminium foam; Experimental testing; Finite element simulation; LS-DYNA

see front matter r 2004 Elsevier Ltd. All rights reserved.

ijimpeng.2004.09.004

ding author. Structural Impact Laboratory (SIMLab), Department of Structural Engineering, Norwegian

f Science and Technology (NTNU), N-7491 Trondheim, Norway. Tel.: +47 73 59 47 82; fax:

1.

ress: [email protected] (A.G. Hanssen).

www.elsevier.com/locate/ijimpeng

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Nomenclature

c1,c2 shape factors for generalised Voce hardeningC0yC6 constants in polynomial equation-of-stateC fourth order tensor of elastic moduliiD isotropic damage variableDC critical damageD rate-of-deformation tensorE Young’s modulushc sheet thickness, component levelhs sheet thickness, tensile test specimenI identity tensorlc element length, componentls element length, tensile test specimenL domain radius for smearingNtb,Stb normal and shear stress capacity on nodal tiebreak interfacep,sm;P pressureQ1,Q2 scale factors for generalised Voce hardeningr damage accumulated plastic strainrD threshold for damage initiationR specific gas constantS damage mechanics material constantt timeT absolute temperatureU internal energy per volumeU0 initial internal energy per volumev0 bird’s impact velocityy strain energy density release rateY0 uniaxial yield stress

Greek letters

a foam yield surface shape factora2;b;g hardening coefficientsg ratio of specific heats� foam model equivalent strain�cr foam hydrostatic failure strain�D compaction strain�m hydrostatic strain�pl; �e accumulated plastic strainee elastic strain tensorm volumetric compression ration Poisson’s ratio

A.G. Hanssen et al. / International Journal of Impact Engineering 32 (2006) 1127–11441128

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nP plastic Poisson’s ratiox element length to thickness ratior densityr0 initial densityrf foam densityrf0 density of foam base material~s effective stresss true stresssij Cauchy stress components foam model equivalent stressse; sVM von Mises equivalent stressstb; ttb normal and shear stress on nodal tiebreak interfacer Cauchy stress tensorrdev deviatoric stress tensorud dynamic viscosity

A.G. Hanssen et al. / International Journal of Impact Engineering 32 (2006) 1127–1144 1129

1. Introduction

Aeronautic structures always fly on the risk of impacting foreign objects. Possible impactscenarios include bird strike, soft body impact (such as rubber) and hard object impact (runwaydebris). Bird strike of aircraft parts causes significant threats to equipment and even to human life.Between 1989 and 1993, 13,427 bird/wildlife strikes have been reported worldwide and in theUnited States the annual damage amounts to millions of dollars [1]. The probability of birdimpact is highest during take off and landing. Also, military aircraft operating frequently in lowaltitudes are highly susceptible to bird strike [1]. For this reason, the worldwide development isfocusing on extensive testing combined with new structural solutions in order to avoid damage ofthe impacted parts of the aircraft [2]. Many new solutions are a result of intensive efforts of thematerial suppliers. One class of materials of interest for bird-strike applications are metallic ororganic foams, hollow sphere assemblies or other cellular structures. Here, various studies havebeen conducted in funded European projects, such as METEOR [3], SAFE [4] and LISA [5]. Thework performed in these projects has shown the potential interest of using such cellular materialsin aeronautic applications for mechanical and acoustic energy absorption.The finite element (FE) method is a powerful tool for development and optimisation of new

structural components. However, modelling the high-speed bird-strike events of aeronautic partsposes several challenges, such as modelling of material failure and which FE formulation to usefor the impacting bird. The recent study by Lagrand et al. [6] has emphasised the need forvalidated simulation tools for aid in design of critical components subject to bird strike. Today,this demand is boosted by the introduction of new and complex materials to the aircraft industry,such as structural foams and composite materials. In their work, Lagrand et al. [6] carried out asensitivity study on Lagrangian and arbitrary Lagrangian Eulerian (ALE) FE techniques toaccurately predict the behaviour of a bird striking a rigid panel. Furthermore, they used the modelto predict the structural behaviour of a riveted component. The study showed that their modelhad problems predicting the failure of the rivets, which is critical when assessing the energy

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Radome shield

Bird

Fig. 1. Bird impacting Radome shield in front of aircraft.


absorbing capacity of the structure. The investigation by Johnson and Holzapfel [7] comprisedexperimental testing as well as bird-strike simulations of fibre reinforced composite structures.Contrary to Lagrand [6] et al., they used the smooth particle hydrodynamic (SPH) FEformulation to represent the impacting bird. The impacting parts were modelled with materialmodels incorporating a failure criterion and the numerical response was encouraging whencompared with experiments.This paper reports experimental tests and FE simulations of a bird striking a double sandwich

panel made from AlSi7Mg0.5 aluminium foam core and AA20204 T3 aluminium sheets. Such acomponent could have a potential for use in the Radome bulkhead section of commercialaircrafts, see Fig. 1, protecting the impacting bird from penetrating into the cockpit area.The objective of this paper was to generate a model with the non-linear, FE code LS-DYNA [8]

to fully represent the bird-strike process of an aluminium foam-based sandwich panel. Materialfailure of the AA2024 T3 aluminium sheets as well as the AlSi7Mg0.5 foam is included in themodel. Section 2 presents the experimental tests carried out on the sandwich components as wellas reference tests of the materials used. Section 3 gives an overview of the FE model, materialidentification and comments the ALE formulation and the ALE–Lagrangian coupling algorithmthat is used for the interaction between bird and sandwich structure. A comparison between theexperimental tests and the model is shown in Section 4. Finally, Section 5 uses the model on aselected case to find the minimum thickness of a simple sandwich panel in order to preventpenetration of the striking bird.

2. Experimental tests

2.1. Component tests

Fig. 2 shows the assembly of the double sandwich panels used for bird-strike testing. Eachsandwich panel is based on an AlSi7Mg0.5 aluminium foam core and two 0.8mm thick AA2024

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Fig. 2. Specification of the test specimens.

Table 1

Test matrix

Test no. Strain gauges Impact velocity Foam density Bird mass Observation

(Yes/no) (m/s) (kg/m3) (kg)

1 Yes 138.1 300 1.81 No penetration

2 No 195.0 300 1.82 No penetration

3 Yes 138.7 150 1.81 No penetration

4 No 138.4 150 1.81 No penetration


T3 aluminium sheets bonded to the core on either side. The assembly consisted of two suchsandwich panels, where the outer and inner panels had a core thickness of 20 and 33mm,respectively, Fig. 2. The density of the foam core was equal for both panels and was varied on twolevels (150–300 kg/m3) according to the test matrix given in Table 1. No bonding was applied inthe interface between the two sandwich panels.The bird impact tests were performed at Saint Gobain Sully, a French company certified to

qualify the AIRBUS windshields against bird impacts. The impact velocity was measured byphotoelectric sensors linked to a frequency-meter. The impacted sandwich panels were fixed bybolts to a heavy support attached to the ground. The impact of the bird was normal to thesandwich panels. Two impact velocities were tested, approximately 140 and 190m/s, see Table 1.As shown here, a total of four tests were carried out. The bird geometry shown in Fig. 2 is anidealised geometry, used for numerical simulations only.For some tests specified in Table 1, the rear sheet of the double sandwich panel was

instrumented by a set of strain gauges centred around the impact area, see Fig. 3. The signalsrecorded during impact provide data for comparison with numerical simulations of Section 4 andare shown in Figs. 10 and 11. There is no obvious explanation for the strain gauge positioning inFig. 3. However, the diameter on which the gauges are positioned roughly correspond to the sizeof the impacting bird. In addition, the gauges are positioned so as to capture strains in differentdirections.

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Fig. 3. Instrumentation of sandwich panel by strain gauges.

Fig. 4. Panels after impact, test 3 (left) and test 1 (right).


The final shape of the specimens after impact is given in Fig. 4. Here, the photos show thebehaviour of the low- (150 kg/m3) and high- (300 kg/m3) density foam panels (tests 3 and 1,respectively). No penetration occurred for either panels, but the low-density foam panel showedclear signs of material failure around the bolts.

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2.2. Material tests

Standard tensile tests of dog-bone shaped specimens with thickness 1.66mm were carried outon the AA2024 T3 material, see Fig. 6 for results. For the foam, compressive tests were done oncubes machined from foam sheets. The AlSi7Mg0.5 aluminium foam was manufactured by HydroAluminium using the continuous casting process (the foam was delivered in 1998; HydroAluminium no longer manufactures aluminium foam). Experimental data from the compressivetests can be found in Fig. 7. Three parallel tests were done for each density, and there is arelatively large amount of scatter evident.

3. Numerical model

The numerical model consists of 6 parts, Fig. 5, and was made using the non-linear, explicit FEcode LS-DYNA (version ls-970). The AA2024 T3 sandwich panel sheets were modelled by thedefault shell element using five section points. The foam core was modelled by the default brickelement. Hourglass control ]5 was used for both shells and bricks. The element size wasapproximately 10mm for both shells and bricks and uniform throughout the structure. The boltsused in the tests to clamp the panels to the fixture were represented by nodal constraints in thenumerical model. Automatic, surface-to-surface contact options were generally used, as well as

Fig. 5. The FE model (exploded view).

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for the adhesive bonding between the core and skin of the individual sandwich panels. Here, thenodal tiebreak failure in the interface was given by the quadratic failure criterion; ðstb=NtbÞ

2þ

ðttb=StbÞ2X1; where stb and ttb are the nodal normal and shear stress components and Ntb and Stb

are the strength of the adhesive in pure tension or pure shear, respectively. Here, N tb ¼ Stb ¼

5MPa was used. The sandwich panels and support were represented by a Lagrangianformulation, whereas the bird and surrounding air was represented by a multi-material arbitraryLagrangian Eulerian (ALE) element formulation. The geometry used for the bird is given in Fig. 8and based on details given by Lagrange et al. [6]. The following sections specify the materialidentification carried out (AA2020 T3, aluminium foam, bird/air) and provides details concerningthe ALE formulation.

3.1. Material identification of AA20204 T3

The AA2024 T3 sheets were represented by material model 104 of LS_DYNA (*MAT_DAMAGE_1). This model is based on the continuum damage theory [9] with associated flow andvon Mises yield criterion where the effective stress ~s is defined as

~s ¼s

1�D; (1)

where D is the isotropic damage variable, 0pDp1; and s is the usual true stress measure. Allconstitutive relations are given in terms of the effective stress ~s instead of the usual stress s (strainequivalence principle). The hardening of the material is expressed by

~s ¼s

1�D¼ Y 0 þQ1 1� expð�c1rÞð Þ þQ2 1� expð�c2rÞð Þ: (2)

Here, r is the damage accumulated plastic strain. Since the incremental plastic work in terms ofusual and effective stress measures has to be equal, i.e. ~s_r ¼ s_�pl; the rate of the damage-accumulated strain is given by _r ¼ ð1�DÞ_�pl: Here _�pl is the usual measure for the rate of theaccumulated plastic strain. An evolution rule of the damage variable D has to be defined. Inmaterial model 104 of LS-DYNA this is given by

_D ¼0 for rprD;

ySð1�DÞ

_r for r4rD;

((3)

rD is the threshold for damage initiation, S is a positive material constant, whereas the strainenergy density release rate y is defined by

y ¼1

2ee : C : ee ¼

s2eRn

2Eð1�DÞ2; Rn ¼

2

3ð1þ nÞ þ 3ð1� 2nÞ

p

se

� �2

: (4)

Rn is referred to here as the triaxiality function, n is the Poisson’s ratio, whereas the hydrostaticpressure is given by p ¼ � 1

3skk: Furthermore, ee is the elastic strain tensor, C the fourth order

tensor of elastic modulii and se the von Mises stress.

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Fig. 6. Identification of the AA20204 T3 material.


Finally, the rupture criterion is given by D ¼ DC; where DC is a material constant denoted asthe critical damage.Identification of the parameters S; rD and DC is best done by inverse modelling of the uniaxial

tensile test, see Fig. 6. However, the FE mesh of the tensile specimen shown in this figure is ingeneral different from the mesh of the component of interest, i.e. the sandwich panel of Fig. 5. Forthe sandwich panel, the element length to thickness ratio xc ¼ lc=hc is 12.5 whereas for the tensilespecimen xs ¼ ls=hs ¼ 1:25: For the post-neck region of the material coupon, the identification ofthe parameters S; rD and DC is dependent on the mesh size. In order to have the same length tothickness ratio for the material coupon and the main component, the inverse modelling of Fig. 6was carried out using a non-local approach invoking the *MAT_NONLOCAL card of LS-DYNA. This approach is based on the non-local theories referred to in [8]. Here, the materialproperties governing the evolution of damage (r and D) are smeared by a weighing function in adomain of radius L. In order to have consistency between the mesh of the sandwich panel and thetensile test, the domain radius is set to L ¼ xc � hs � 20mm:The final material identification for AA2024 T3 in uniaxial tension is given in Fig. 6. Any

possible material strain-rate effects have been neglected. The following material data referring tothe above equations were used: r ¼ 2700kg=m3; E ¼ 70GPa; n ¼ 0:3; Y 0 ¼ 364:5MPa; Q1 ¼

334:7MPa; c1 ¼ 6:16; Q2 ¼ 0MPa; c2 ¼ 0; rD ¼ 0:18; S ¼ 0:5MPa and DC ¼ 0:1:

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3.2. Material identification of aluminium foam

The aluminium foam was modelled by material model 154 of LS-DYNA (*MAT_DESH-PANDE_FLECK_FOAM), see Reyes et al. [10] and Deshpande and Fleck [11]. The yieldfunction F is defined by F ¼ s� sY where the equivalent stress s is given by

s2 ¼s2VM þ a2s2m1þ a=3

� �2 : (5)

Here sVM is the von Mises effective stress given by sVM ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi32r

dev : rdev

q: sm and rdev are the

hydrostatic and deviatoric stress tensors, respectively, i.e. sm ¼ trðrÞ and rdev ¼ r� smI:The parameter a ð0pa2p9

2Þ defines the shape of the yield surface and can be linked to the plastic

Poisson’s ratio np by a2 ¼ 92ð1� 2npÞ=ð1þ npÞ:

The current yield stress (hardening) is expressed as

sY ¼ sp þ g�

�Dþ a2 ln

1

1� ð�=�DÞb

!; (6)

where sp is the plateau stress and a2; g and b are hardening parameters. Here � is the equivalentstrain, energy conjugate to the equivalent stress s; given by

�2 ¼ 1þa3

� �2� ��2e þ

1

a2�2m

� ; (7)

where �e and �m are the von Mises and hydrostatic effective strains, respectively. The compactionstrain �D is defined from uniaxial compression as

�D ¼ �9þ a2

3a2ln

rfrf0

� �; (8)

where rf is the foam density and rf0 is the density of the base material. Failure (element erosion)takes place when a positive value of the hydrostatic strain �m exceeds the volumetric failure strain�cr

m ; i.e. �mX�crm :

Results from modelling the uniaxial compression of a foam cube compared to the experimentaldata points are given in Fig. 7. Any possible strain-rate effects have been omitted. For foamdensity rf ¼ 150kg=m3 the following material properties were used: E ¼ 300MPa; np ¼ 0:05;a ¼ 2:1; g ¼ 1:19MPa; �D ¼ 2:89; a2 ¼ 52:1MPa; b ¼ 3:26; sp ¼ 0:93MPa; �cr ¼ 0:1: For thehigh-density foam (rf ¼ 300 kg=m3), the identified parameters are: E ¼ 1500MPa; np ¼ 0:05; a ¼2:1; g ¼ 6:10MPa; �D ¼ 2:20; a2 ¼ 38:1MPa; b ¼ 3:1; sp ¼ 4:41MPa; �cr ¼ 0:1:

3.3. Material identification of bird/air

Material number 9 of LS-DYNA (*MAT_NULL) calculates the pressure P from a specifiedequation-of-state. Only viscous deviatoric stresses are considered, i.e. the stresses are given by

r ¼ 2udD� PI; (9)

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0 0.2 0.4 0 0.8

Nominal strain Nominal strain

0

1

2

3

4

5

Nom

inal

str

ess

(M

Pa

)

Nom

inal

str

ess

(M

Pa

)

0 0.2 0.4 0.6 0.8 1

0

5

10

15

20

25

Experimentalpoint

LS-DYNA

F150 kg/m3

Foam density:300 kg/m3

0.6

Foam density: Foam density:300 kg/m3

Fig. 7. Compressive reference data for aluminium foam.

Fig. 8. ALE representation of bird and air.


where ud is the dynamic or absolute viscosity, D the rate-of-deformation tensor and I the identitytensor.The equation-of-state was defined by card *EOS_LINEAR_POLYNOMIAL of LS-DYNA,

where the pressure P is expressed as

P ¼ C0 þ C1mþ C2m2 þ C3m3 þ ðC4 þ C5mþ C6m2ÞU ; (10)

where U is the internal energy per volume. The compression of the material is defined by theparameter m ¼ r=r0 � 1; where r and r0 are the current and initial density of the material,respectively.

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The bird material was identified for this model using the material properties specified byLagrange et al. [6]; C0 ¼ 0; C1 ¼ 2250MPa; C2:::C6 ¼ 0 and ud ¼ 0:001Ns=m2: The total mass ofthe bird used in the experiments was 1.8 kg, Section 2, which gives the bird an initial density ofr0=950 kg/m3 (based on the geometry of Fig. 8).The air was modelled as an ideal gas by setting C0 ¼ C1 ¼ C2 ¼ C3 ¼ C6 ¼ 0 and C4 ¼ C5 ¼

g� 1; where g is the ratio of specific heats, i.e. specific heat at constant pressure divided by specificheat at constant volume. In this case the pressure P is given by

P ¼ ðg� 1Þrr0

U ; U ¼r0RT

g� 1; (11)

where the internal energy U is defined by the absolute temperature T (in Kelvin) and the specificgas constant R ¼ 287 J=kgK: The initial internal energy U0 of the gas was defined for atemperature of T ¼ 293K: Equivalently, LS-DYNA card *EOS_IDEAL_GAS can be used tomodel the air.

3.4. ALE formulation and ALE–Lagrange coupling

The bird was expected to undergo too large deformations for a pure Lagrangian description ofmotion to be a feasible option. For that reason a multi-material ALE formulation was chosen forthe treatment of the bird. Multi-material implies that each element in the mesh is allowed tocontain a mixture of two or more materials, in this case bird material and air. The ALEformulation means that the mesh is allowed to move independently to the material flow. In thiscase the mesh was assigned to translate and expand to enclose most of the bird materialthroughout the simulation process.To solve the governing equations posed in an ALE reference system, LS-DYNA relies on

a so-called operator split technique where each time step is split into a Lagrangian phaseand an advection phase. In the Lagrangian phase, the FE model is treated as if it waspurely Lagrangian. That is, the mesh is forced to follow the motion of the material flow.n the advection phase the nodes of the mesh are repositioned to new, preferred, locationsand the solution is mapped from the old configuration onto the new one. A spatially secondorder accurate advection algorithm, referred to as the van Leer method, was used inthis work. Both the operator split technique and the van Leer advection algorithm aredescribed in [12].Fig. 8 shows how the bird and the surrounding air have been represented in the model. The air

is initially pressurised at 1 bar. An external pressure of the same magnitude is applied to act on allexternal element faces of the ALE mesh.A penalty-based ALE–Lagrangian coupling algorithm was invoked to communicate contact

forces between the bird material in the ALE mesh and the Lagrangian target. The function of theALE–Lagrangian coupling algorithm is very similar to the one of a classical penalty-based contactalgorithm. The contact pressure is simply proportional to the distance the bird material penetratesthe target. Aside from numerical errors, the penalty-based coupling algorithm conserves bothtotal energy and momentum, an important feature in impact analyses. The implementedalgorithm is briefly described in [13].

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4. Numerical results

The strain-gauge instrumented tests 1 and 3, Table 1, were simulated using the model describedabove. The surface strains from the simulations have been extracted from the elements shown inFig. 9 with locations corresponding to the physical positioning of the strain gauges. Figs. 10 and11 compare the surface strains taken from the numerical model with the experimental recordings.The experimental results have been grouped in the following manner: Gauges 1–3, Gauges 4 and 5and finally Gauge 6. Gauge 7 is plotted independently and Gauge 8 is not included in thecomparison. As seen, the experimental results within each group consisting of more than onestrain gauge are relatively consistent. The comparison between experiments and simulations givenin Figs. 10 and 11 was done in the following manner: Gauges 1–3 were compared to the surfacestrain in the x- and y-directions for one of the four elements in Selection A, Fig. 9 (all elements inthe group gave approximately the same readings). Gauges 4 and 5 were compared to the surfacestrain in the x-direction of Selection B, whereas Gauge 6 was compared to the surface strain in x-direction of Selection C. Finally, Gauge 7 was compared to the surface strain in y-direction ofSelection C.There is a fair, overall agreement between model and experiments, Figs. 10 and 11, at least for

the first millisecond of the event. For the low-density foam core, the numerically based strainstend to give higher values than what can be observed experimentally. For the high-density foamcores, the prediction is better albeit a higher number of strain gauges saturated earlier herecompared to the tests on the low-density foam panels. The ideal bird, Fig. 8, may be more cigarshaped when compared to the real bird used in the tests, which may offer an explanation for whyhigher strains are observed in the model for a number of strain gauges; the real bird may spreadthe load over a larger area, thus reducing the local strains in the central impact area.Fig. 12 shows a sequence of the deformation behaviour of the impacted panels. From the

moment of impact, the bird is gradually squashed into the panel. No penetration occurs in themodel as for the experiments. Moreover, the model is able to describe the local material failure inAA2024 T3 skin and low-density foam core that takes place near the bolts, Fig. 13, which issimilar to the experimental observations.

Fig. 9. Extraction of surface strains from simulations.

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-1

-0.5

0

0.5

1S

trai

n (%

)

Gauges 1,2 and 3Simulation

0 0.5 1.5 2 2.5 3time (ms)

-1

-0.5

0

0.5

1

Str

ain

(%)

Gauge 7Simulation

-1

-0.5

0

0.5

1

Str

ain

(%)

Gauges 4 and 5Simulation

-1

-0.5

0

0.5

1

Str

ain

(%)

Gauge 6Simulation

x-direction

y-direction

1

0 0.5 1.5 2 2.5 3

time (ms)

1

0 0.5 1.5 2 2.5 3

time (ms)1

0 0.5 1.5 2 2.5 3

time (ms)

1

Fig. 10. Comparison of surface strains, low-density sandwich panels.


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0 0.5 1 1.5 2 2.5 3time (ms)

0 0.5 1 1.5 2 2.5 3time (ms)

0 0.5 1 1.5 2 2.5 3

time (ms)

0 0.5 1 1.5 2 2.5 3

time (ms)

-1

-0.5

0

0.5

1

Str

ain

(%)

-1

-0.5

0

0.5

1

Str

ain

(%)

-1

-0.5

0

0.5

1

Str

ain

(%)

-1

-0.5

0

0.5

1

Str

ain

(%)

Gauges 1,2 and 3Simulation

Gauge 7Simulation

Gauges 4 and 5Simulation

Gauge 6Simulation

x-direction

y-direction

Fig. 11. Comparison of surface strains, high-density sandwich panels.


5. Case study—simple sandwich panel

In order to illustrate the potential of the model for structural design, a simple case study isshown. Fig. 14 shows a simple sandwich panel with a low-density foam core (150 kg/m3) and a0.8mm AA20204 T3 sheet on each side. The bird impacts the panel at the centre with an initial

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Fig. 12. Sequence from bird impact on low- and high-density sandwich sheets.

Fig. 13. Details at t ¼ 3:5ms; low-density sandwich panel.


velocity of 190m/s. All edges of the sandwich panel are clamped. The material properties are asbefore. The simple problem is to increase the thickness of the foam core, keeping the otherparameters constant, until a thickness is reached where no penetration of the bird occurs. Fig. 15shows the results. The simulations started with a core thickness of 30mm which was increasedstepwise. At 150mm core thickness the bird is fully arrested by the panels. Note how the modeldescribes a shear-type failure of the foam core coupled with material failure in the AA20204 T3skins.

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Fig. 14. Sandwich panel selected for the case study.

Fig. 15. Results from case study.


6. Conclusions

The study has showed the potential of using the finite element method in predicting the failureof structural components in bird-strike events. The component of interest was a double sandwichpanel made by assembling two individual sandwich panels on top of each other. The aluminiumskins of each panel was bonded to the foam core, but no bonding was used in the interfacebetween the two individual panels. It was found necessary to model the bird by a multi-materialALE formulation since the bird is heavily deformed during the event. The constitutive modelsapplied for the sandwich panel included failure and was identified from experiments. A fluidstructure algorithm was used to ensure proper contact between the impacting bird and thestructure and worked well also for cases when material failure occurred. The numerical model ofthe impacted sandwich panel was validated by experimental tests. It was found that the model

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represented local strains, global deformation behaviour and local occurrences of failure fairlywell. No complete penetration of the panels took place in the experiments (as for the model), butfor a full validation it would have been preferable to include cases of complete penetration. Toillustrate the potential of the model for full penetration, a case study of a simple sandwich panelwas done. Using this model, the minimum foam-core thickness in order to avoid penetration ofthe bird could be found.

Acknowledgements

The authors would like to thank the EC which founded part of this work through Contract No.G5RD-CT-2001-00484.

References

[1] York DL, Cummings JL, Engeman RM, Wedemeyer KL. Hazing and movements of Canada geese near

Elmendorf Air Force Base in Anchorage, Alaska. Int Biodeterior Biodegrad 2000;45(3–4):103–10.

[2] Becker H, Andersen S. Wings for the giant. Air Space Europe 1999;1(2):83–6.

[3] METEOR, EU Brite Euram. Lightweight metal foam components for the transport industry, 1998–2001.

[4] SAFE, EU Craft Project. Development of lightweight shock absorbent component made of a metallic hollow

sphere structure for the transport industry, 1998–2001.

[5] LISA, EU Framework 5. Lightweight structural applications based on metallic and organic foams, 2002–2005.

[6] Lagrand B, Bayart A-S, Chauveau Y, Deletombe E. Assessment of multi-physics FE methods for bird strike

modeling—application to a metallic riveted airframe. Int J Crashworthiness 2002;7/4:415–28.

[7] Johnson AF, Holzapfel M. Modelling soft body impact on composite structures. Compos Struct

2003;61(1–2):103–13.

[8] LS-DYNA keyword user’s manual. Livermore Software Technology Corporation. Version 970, 2003.

[9] Lemaitre J. A course on damage mechanics. 2nd ed. Berlin: Springer; ISBN 3-540-60980-6, 1996.

[10] Reyes A, Hopperstad OS, Berstad T, Hanssen AG, Langseth M. Constitutive modeling of aluminum foam

including fracture and statistical variation of density. Eur J Mech A/Solids 2003;22(6):815–35.

[11] Deshpande VS, Fleck NA. Isotropic constitutive models for metallic foams. J Mech Phys Solids 2000;48:1253–83.

[12] Benson DJ. Computational methods in Lagrangian and Eulerian hydrocodes. Comput Methods Appl Mech Eng

1992;99:235–394.

[13] Olovsson L. On the arbitrary Lagrangian–Eulerian finite element method. Linkoping Studies in Sci. Tech., Dissert.

No 635, 2000.

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