bird strike - a review

8/20/2019 Bird Strike - A Review

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Review

Computational methods for bird strike simulations: A review

Sebastian Heimbs ⇑

EADS – European Aeronautic Defence and Space Company, Innovation Works, 81663 Munich, Germany

a r t i c l e i n f o

Article history:

Received 16 February 2010

Accepted 15 August 2011

Available online 9 September 2011

Keywords:

Bird strike simulation

Soft body impact

Fluid–structure interaction

Lagrangian

Eulerian

SPH

a b s t r a c t

Bird strikes are a major threat to aircraft structures, as a collision with a bird during flight can lead to

serious structural damage. Computational methods have been used for more than 30 years for the

bird-proof design of such structures, being an efficient tool compared to the expensive physical certifica-tion tests with real birds. At the velocities of interest, the bird behaves as a soft body and flows in a fluid-

like manner over the target structure, with the high deformations of the spreading material being a major

challenge for finite element simulations. This paper gives an overview on the development, characteris-

tics and applications of different soft body impactor modeling methods by an extensive literature survey.

Advantages and disadvantages of the most established techniques, which are the Lagrangian, Eulerian or

meshless particle modeling methods, are highlighted and further topics like the appropriate choice of

impactor geometry or material model are discussed. A tabular overview of all bird strike simulation

papers covered by this survey with detailed information on the software, modeling method, impactor

geometry, mass and velocity as well as the target application of each study is given in the appendix of

this paper.

2011 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2094

2. Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2095

3. Substitute bird materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096

4. Test data for bird model validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2096

5. Bird modeling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2097

5.1. First bird strike simulations: bird as pressure function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2097

5.2. Lagrangian bird impactor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2097

5.2.1. Characteristics of Lagrangian modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2097

5.2.2. Application of Lagrangian model for bird strike simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2098

5.3. Eulerian bird impactor model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2098

5.3.1. Characteristics of Eulerian modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2098

5.3.2. Application of Eulerian model for bird strike simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2100

5.4. SPH bird impactor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2100

5.4.1. Characteristics of SPH modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2100

5.4.2. Application of SPH model for bird strike simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21015.5. Comparison of different bird modeling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2101

5.6. Summary on bird modeling methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2102

6. Impactor geometry for bird strike simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2102

7. Bird impactor material models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2103

8. Contact calculation in bird strike simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104

9. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104

Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2104

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2109

0045-7949/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.compstruc.2011.08.007

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E-mail address: [email protected]

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a suitable bird model is often the main problem in the numerical

simulation of bird strike. Starting with relatively simple nonlinear

calculations and a pressure load applied to the target structure in

the 1970s, complex fluid–structure interactions are treated today

with explicit simulation codes and high performance computing

(HPC). Besides load cases like water ditching or crashworthiness

evaluations in drop test simulations, bird strike simulations are

among the major load cases for the aircraft industry treated withexplicit finite element (FE) analysis codes today.

Therefore, many studies and investigations on bird strike mod-

eling have been conducted in the past and a lot of papers on differ-

ent modeling methods have been published in the technical

literature. Most interestingly, this evolution from simple to com-

plex and accurate methods did not lead to the establishment of

one generally accepted bird impactor modeling approach. Instead,

there are still at least three techniques today, which are widely

used, each having its own advantages and disadvantages. There-

fore, it can be difficult for the analyst to have an overview and to

decide for an appropriate modeling method.

The intention of the current paper is to give this overview on

computational methods for bird strike simulation by an extensive

and so far unique literature review on the topic of soft body bird

impactor modeling. Although a lot of in-house bird strike research

work is conducted in aerospace companies and documented in

internal reports, the focus of this literature review is on generally

accessible papers and publications. More than 190 papers have

been evaluated in a meticulous study, giving a considerable

impression of the progress in bird strike modeling over the last

30 years. Though, a guarantee on completeness is by no means gi-

ven. After some introductory words on the hydrodynamic basics

for bird impactor modeling, typical substitute bird materials used

and available test data for model validations, the focus will be on

the successive development of different numerical methods for

the bird modeling. The three most established methods (Lagrang-

ian, Eulerian and meshless particle modeling) will be introduced

in more detail, highlighting their advantages, disadvantages and

potential applications. Additional topics like the appropriate birdimpactor geometry, material model and contact algorithm are ad-

dressed. Furthermore, a tabular overview of all bird strike analysis

publications with detailed information on the software, modeling

method, impactor geometry, mass and velocity as well as the tar-

get application of each paper is given in the appendix, being a

big help for aeronautical analysts searching for comparable litera-

ture for their specific bird strike load case scenario.

2. Theoretical background

According to [20], the projectile response during an impact can

be divided into five categories as a function of the impact velocity:

elastic, plastic, hydrodynamic, sonic or explosive. During an elastic

impact, the internal stresses in the projectile are below the mate-rial strength so that it will rebound. With increasing impact veloc-

ity, plastic response of the impactor begins but the material

strength is still sufficient to prevent a fluid-like behavior. A further

increase of impact velocity causes internal stresses to exceed the

projectile’s strength and fluid-like flow occurs. At this impact

velocity, the material density and not the material strength deter-

mines the response of the impactor. This flow behavior of real birds

can typically be observed in high-speed films of impact tests.

Therefore, the bird impactor is treated as a so-called ‘soft body’

at the velocities of interest, since the stresses that develop within

the bird are significantly higher than its own strength. The load

is spread over a relatively large area during the impact.

Pioneering work on the characterization of bird impact loads on

flat targets has been performed by Wilbeck and Barber [21–24].Besides extensive experimental studies to assess the flow behavior

and pressure loads, the basics of the hydrodynamic theory of a soft

body impacting a flat target were derived, which are briefly indi-

cated here.

The impact behavior consists of four main phases: (a) initial

shock at contact, (b) impact shock decay, (c) steady flow and (d)

pressure decay (Fig. 2) [20,25]. If the impactor with an initial veloc-

ity u0 hits a surface, the material at the contact point is instanta-

neously brought to rest and a shock wave with the velocity us isgenerated. The orientation of this wave front is parallel to the sur-

face and the running direction is perpendicular to the surface,

propagating up the impactor body. A significant pressure gradient

develops at the outer surface because of the shock-load on the one

side and the free surface on the other side. This leads to an outward

acceleration of the material particles and a release wave is formed,

which propagates inwards towards the centre of impact, interact-

ing with the shock wave. This release wave causes a significant de-

crease in the pressure at the impact point. Therefore, the high

initial pressure peak at the centre of impact lasts less than a micro-

second (Fig. 3) [26,27]. After several reflections of the release

waves, the material flows steadily, leading to a constant pressure

and velocity in the impactor [23]. The existence of steady flow de-

pends on the length/diameter ratio of the impactor. Since for a very

short impactor the impact event will be over before steady flow

can establish, a length/diameter ratio of 2 is recommended. It

should be noted that the velocities of the shock and release waves

are much greater than the initial velocity of the impactor. During

the phase of steady flow, the shock wave trace is constantly weak-

ened by the release waves until the bird and its trace are reduced

to zero through the release process. A typical pressure curve for

such a soft body impact on a rigid target plate is depicted in Fig. 3.

The initial pressure peak in the contact point in a perpendicular

impact is typically referred to as the Hugoniot pressure P H :

P H ¼ q0u0us; ð1Þ

with q0 as the initial density of the impactor.

Fig. 2. Illustration of shock and release waves in soft body impactor (according to[23]).

S. Heimbs / Computers and Structures 89 (2011) 2093–2112 2095


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The steady-flow pressure P S can be estimated by the Bernoulli

relationship:

P S ¼1

2q0u20: ð2Þ

The total duration t D of the impact can be approximated by thetime needed for the impactor to flow through its own length L:

t D ¼ L

u0: ð3Þ

3. Substitute bird materials

For bird strike certification tests on aircraft components real

birds have to be used, typically dead or sedated chickens. However,

the use of real birds is not ideal due to the large scatter between

individual tests. As only the mass is defined by the certification

regulation, the species may vary, having different body densities.

This can have a significant effect on the impact load. The irregular

shape of the bird may also pose difficulties in striking the desiredtarget point on the structure [28]. For these and further reasons

like hygiene, many companies use artificial birds or substitute

birds for pre-certification impact testing, leading to advantages in

convenience, cost and reproducibility [29]. The substitute bird

shall not copy the real bird itself with its flesh and bones, but it

should reproduce the same pressure loading during impact as a

real bird. The substitute bird geometry and material have to be se-

lected appropriately for this purpose.

Typical substitute artificial birds have a simplified regular

geometry like a cylinder, a cylinder with hemispherical ends, an

ellipsoid or a sphere, representing the torso of the bird. The influ-

ence of the impactor geometry is discussed in a later chapter.

Several impact tests were conducted with wax, foam, emulsion,

beef, rubber, neoprene and gelatin as substitute materials for birds[16,23,30]. It could be concluded from these studies that soft mate-

rial substitutes that have the specific gravity of water produced

loading profiles similar to those of real birds. Gelatin, or porous

gelatin, with the specific gravity of water, reproduced the behavior

of a real bird with a high degree of accuracy. The corresponding

pressure curves during an impact on a rigid plate correlate to the

real bird’s pressure curve. For this reason, gelatin is today the most

frequently used substitute bird material in both experimental tests

and numerical simulations [16].

4. Test data for bird model validation

Once an appropriate numerical bird impactor model is devel-

oped, it has to be validated against experimental data before usingit for impact simulations on complex aircraft components.

For this purpose, it is common practice to simulate the impact

on a rigid, flat plate and to assess qualitatively the flow behavior

for comparisons with high speed films and quantitatively the pres-

sure curve for comparisons against data from pressure transducers.

Physical tests are typically performed with a high-powered gas

cannon, which is used for bird strike tests since the mid 1950s.

The component is mounted on a test rig and the bird is fired at a

realistic operational velocity onto the target structure. Inside thecannon, a real bird or substitute bird is placed in a cylindrical,

open-ended carrier, a so-called sabot, which is accelerated by gas

pressure to the required velocity and separates from the projectile

before impact [16].

Because the availability of test data is very limited, the majority

of all studies in the literature use the experimental study of Barber

et al. and Wilbeck [21,23,24] from the late 1970s for validations.

They conducted impact tests on a rigid plate with pressure trans-

ducers mounted on the surface, using different impactors like real

birds, beef, neoprene, rubber, gelatin and porous gelatin. The imp-

actors of different weights, except the real birds, had a cylindrical

shape and velocities of 100–300 m/s. The pressure–time-curves,

measured by the centre pressure transducer with a sampling

frequency of 300 kHz, were taken as the reference curves for

numerous model validations. However, uncertainties of these 30

years old test data arise from the fact that the piezoelectric quartz

pressure transducers used in these studies were not designed for

transient impact loads as they had no adequate acceleration com-

pensation with noise occurring in the curves. Furthermore, their

resonance frequency was about 300 kHz, leading to resonance-in-

duced overshots in some of the curves. The accuracy of the mea-

surements was also limited by the finite frequency response of

the transducers, which prevented measurements of rise times of

less than 5 ls. One additional point is the fact that the distance be-

tween the gas gun and the pressure plate is not known and no

information is given, if the geometrical consistency of the fluid-like

impactor was maintained at the time of impact or if the impactor

was already distorted during the time of flying, as it was observed

in later studies [19]. Lavoie et al. [31,32] remind that the experi-mental pressure data by Wilbeck should only be seen as a refer-

ence for the general behavior rather than as a tool of evaluation.

More recent data were generated by the GARTEUR bird strike

group (Group for Aeronautical Research and Technology in Eur-

ope), which were used for validations in [3,33–35], but those re-

sults are not available to the public.

In order to provide new test data, Lavoie et al. [36] have per-

formed new tests lately. A 1 kg cylindrical impactor with hemi-

spherical ends was used for impact tests at 0 and 30. However,

the authors put those experimental data into question, since the

pressure curves are about 3–4 times higher than theoretically

expected. Furthermore, the transferred energy is higher than the

initial energy. Hence, values of the tests were corrected by normal-

izing them. No final explanation of this error could be given, mak-ing the use of these data for model validations questionable.

Some experimental data of bird strike tests on wing leading

edges or windshields can be found in the literature, but they typi-

cally only apply for the specific configuration of the respective

study and cannot be applied for general bird impactor model vali-

dation purposes.

Besides the pure validation of bird impactor models in impact

simulations on rigid plates, it is proposed in [37] that additional

reference tests on a test rig with a bird splitter should be used

for the validation of the numerical model, if the bird splits during

the simulation, e.g. during the impact on a sharp leading edge of

military aircraft. Moffat and Cleghorn [38], Kamoulakos [39] and

Smojver and Ivancevic [40] advise to include impact simulations

on deformable metallic plates with plastic deformations for valida-tion, as they are documented in [41–43], to calibrate the impactor

Fig. 3. Typical pressure curve for normal soft body impact on a rigid plate.

2096 S. Heimbs / Computers and Structures 89 (2011) 2093–2112


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model for realistic impact damages. Soft body impact tests on fi-

ber-reinforced composite plates are documented in [44–49].

5. Bird modeling methods

Impact simulations of a soft body that is highly deformed dur-

ing the analysis are a major challenge for FE codes. The following

chapter summarizes the development of different numerical ap-proaches to cope with this challenge and characterizes the model-

ing methods with their advantages and disadvantages.

5.1. First bird strike simulations: bird as pressure function

While the first theoretical bird strike investigations were based

on pure analytical calculations [50], the finite element method was

adopted as a bird strike analysis tool in the late 1970s with pio-

neering work conducted by the US Air Force research laboratories

[10]. However, the requirements of complex bird strike analyses

for existing FE codes at the time of 1975 were too demanding, be-

cause of the large deflections, high nonlinearity of the plastic target

materials typically used, three-dimensionality and the high loading

rate [10]. Linear FE codes like the program IMPACT, developed in1977, were not able to deliver acceptable numerical predictions,

with deviations of 50% to experimentally measured strains. In

1978 the nonlinear FE code MAGNA was developed and applied

for bird strike simulations on windshields [10], accounting for very

severe geometrical and material nonlinearities. For the bird impact

load a uniform pressure vs. time curve was applied in normal

direction, which represents the nearly constant steady-flow pres-

sure observed in bird impact tests on rigid plates, neglecting the

initial pressure peak and tangential loads. This pressure was ap-

plied as a uniform force over a specified ‘bird impact footprint’ area

[51]. The same approach was used in [52] for bird impact analyses

on fan blades with the program MARC. In [53–59] a bilinear or

stepwise instead of a uniform pressure–time-curve was used to

cover the initial pressure peak for bird strike simulations withthe codes NONSAP, DYNA3D, BASIS and BINA, respectively. Ref.

[60] used a trilinear pressure function to approximate the pressure

peak and steady-flow pressure and scaled this pressure curve as a

function of the radius to the central point to cover the spreading.

Refs. [30,61] take the spreading of the bird into account by increas-

ing the oval ‘footprint’ area with time.

In contrast to pure bird strike loads on rigid plates, it was early

understood that interactive effects must be included in the solution

of deformable targets, i.e. the applied loads are a function of the

structural response (coupled fluid–structure interaction) [12,51,

52,55,62]. Typically, subroutines were used to update the bird im-

pact pressure continually during the solution. McCarty used this

approach within the code MAGNA for bird strike analyses on wind-

shields of numerous aircraft like theF-16 [51], TF-15 [12], T-38 [63],

T-46A [64] and the Space Shuttle orbiter [65,66], Leski etal. [60] for

the Russian fighter Su-22, Wen[67] forthe Chinese Y-12 aircraft andBoroughs [68] for the Learjet 45.

5.2. Lagrangian bird impactor model

First attempts to actually model the soft body impactor with

Lagrangian elements instead of applying pressure loads were doc-

umented in 1984 by Brockman [69–71] and West [72], using eight-

node solid elements, explicit time integration and rezoning or

mesh regeneration to avoid excessive mesh distortion. A contact

algorithm covers the fluid–structure interaction in this case. For

the transient bird strike problem the conditionally stable explicit

central-difference time integration is typically seen to be more

appropriate than the implicit integration procedure. Stability re-

quires the use of time steps shorter than the wave propagationtime in the smallest element of the model [73]. However, since

for some problems the dynamic implicit solver can be more effi-

cient, implicit bird strike simulations might for some specific cases

be a good contender to the explicit methods.

5.2.1. Characteristics of Lagrangian modeling

The Lagrangian modeling method is the standard approach for

most structural finite element analyses. The nodes of the Lagrang-

ian mesh are associated to the material and therefore each node of

the mesh follows the material under motion and deformation

(Fig. 4a). The boundary of the body is always clearly defined, since

the boundary nodes remain on the material boundary, leading to a

simplified definition of boundary conditions. This approach is typ-

ically used for solid materials.The major problem of Lagrangian bird impactor models are the

severe mesh deformations. Large distortions of the elements may

lead to inaccurate results, severe hourglassing and even error ter-

mination due to negative volume elements [5,74–78]. In [79] it is

highlighted that large distortion of elements may introduce an arti-

ficial stiffening effect into the soft body finite element model, neg-

atively affecting the impact pressure curve. Furthermore, the time

step in explicit calculations drastically decreases, when the solid

Fig. 4. Different finite element modeling methods for soft body projectiles.



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elements are compressed to such an extent, since the time step de-

pends on the shortest element length in the model. The element

deformation in a Lagrangian bird model is shown in Fig. 5.

Several choices exist for dealing with the mesh distortion prob-

lem, including adaptive remeshing or element erosion. Adaptive

remeshing involves remeshing the region of severe mesh tangling.

According to [16], this mapping procedure often increases the

numerical errors associated with the approximation and may becomputationally expensive. In [80] elements are deleted from the

calculation, when they reach a defined degree of flattening, which

is referred to as element erosion. Zhu et al. [81] used a shear failure

criterion for element deletion. The deletion of highly distorted ele-

ments prevents numerical problems, and was often adopted in

other studies, with the argument that most of the momentum of

those elements is probably already transferred to the structure

[76,82]. In contrast, Lavoie et al. [31] and Chandra et al. [83] report

that especially for finely meshed Lagrangian impactors with ele-

ment erosion a large part of the mass is eroded during the simula-

tion, which makes it very difficult to obtain accurate results.

However, the mass can be retained after element deletion by lump-

ing it at the free nodes still interacting with the structure [84–86].

With this approach of element erosion even the splitting of a bird

can be modeled with Lagrangian elements [37,84,87,88]. However,

Castelletti and Anghileri [75] remind that the numerical–experi-

mental correlation gets worse, when a failure criterion is intro-

duced, compared to a good correlation without failure criterion,

without providing any further details on the criterion used or its

effect. Another typical problem arising from element erosion is

the artificial oscillations in the contact forces due to the discretised

nature of the simulated contact algorithms, especially for coarse

meshes. Once the frontal elements are deleted, the contact force

will decrease dramatically until the impactor comes into contact

again with the target, and this introduces artificial noise into the

contact forces [33]. This can only be reduced by using very fine

meshes [3]. A severe influence of the mesh density in the Lagrang-

ian impactor was also identified in [31,86]. Georgiadis et al. [5]

conclude that the Lagrangian approach remains an impracticalway to model bird strike.

5.2.2. Application of Lagrangian model for bird strike simulations

Lawson and Tuley [89], Schuette [90] and Niering [91] adopted

this approach with Lagrangian elements for the impactor in the

late 1980s and early 1990s for explicit bird strike simulations on

engine fan blades with DYNA3D. The results of Niering [91] indi-

cated that internal friction in the bird material should be

accounted for, otherwise the pressure maxima occur at the rim

of the impact area and not in the impact centre. This internal fric-

tion was introduced by Niering with a viscous material law in LS-

DYNA in terms of compression and shear viscosity.

The Lagrangian method became the standard approach for bird

impactor modeling for the next decade and beyond. It was used by

several researchers for impact simulations on windshields [11,81,

85,92–100], engine fan blades [3,33–35,82,101–106], helicopterblades [87], aircraft radomes [14,26,107], the forward bulkhead be-

hind the radome [108], fuselage panels [25,109], composite plates

[45,47,83] and wing/tail plane leading edges [28,73,83–85,107,

110–125].

5.3. Eulerian bird impactor model

The major limitation of the Lagrangian model with respect to

the flow behavior is excessive mesh distortion, hence reduced time

step. A promising alternative is the Eulerian modeling technique,

which is mostly applied to the simulation of fluid behavior.

5.3.1. Characteristics of Eulerian modeling

In the Eulerian formulation, the mesh remains fixed in space

and the material under study flows through the mesh (Fig. 4b)

[76]. Since the mesh does not move, mesh deformations do not oc-

cur and the explicit time step is not influenced. Stability problems

due to excessive element deformation do not occur. This approach

is typically used for fluid materials and flow processes. Each ele-

ment has a certain volume fraction of different materials, those

can be for example a fluid material and void, or even other mate-

rials. This means that each element may be partially filled with

the fluid material. The disadvantage of this approach is that the

body’s boundary is not exactly defined, and depends on the mesh

size. Visualization tools in the post-processing software can be

used to roughly estimate the outer boundaries.

Since in a bird strike simulation typically only the impactor is

modeled as a fluid-like body with Eulerian elements and the target

as a solid structure with Lagrangian elements, a coupled Eulerian–

Lagrangian approach is used for this fluid–structure interaction

problem. Since the mesh in the classical Eulerian technique is fixed

in space, the computational domain should cover not only the re-

gion where the material currently exists, but also additional void

space to represent the region where material may exist at a later

time of interest (Fig. 6). Therefore, the computational domain for

structural analysis with the Eulerian technique is much larger than

with the Lagrangian approach [16]. In general, the computational

Fig. 5. Bird strike simulation on rigid plate with Lagrangian impactor model.



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cost of the Eulerian model is relatively high, due to the high num-

ber of elements and the cost-intensive calculation of element vol-

ume fractions and interactions [127]. Typically, the element size of

the Eulerian mesh has to be defined very small in order to achieve

accurate results [79]. The Eulerian formulation is also not free from

numerical problems. There are well-known dissipation and disper-

sion problems associated with the flux of mass between elements

(numerical leakage) [94,101,126–129]. McCallum and Constanti-

nou [130] conclude that the total energy decreases by approxi-

mately 6% from the starting value, which is associated with a

loss of energy in the contact interface during the bird strike simu-

lation. Lavoie et al. [36] even report a loss of 25% of the bird mass

during the impact simulation.

In contrast to the classical Eulerian modeling with a fixed Eule-rian mesh, the Arbitrary Lagrangian–Eulerian (ALE) formulation

was adopted to make the simulation more efficient. The ALE meth-

od is basically similar to the classical Eulerian method, but the

surrounding Eulerian box can move and stretch if needed and is

not fixed in space (Fig. 4c) [79]. Depending on the current position

of the bird material in space, the geometry and position of the

Eulerian background mesh is consistently updated. Since the back-

ground mesh can move in the same direction as the projectile, the

number of elements for the computational domain can signifi-

cantly be reduced, leading to computational time savings, espe-

cially when motion of the material covers a wide region in space

[75,79]. However, it has to be kept in mind that through the

spreading of the bird material the lateral expansion of the Eulerian

box is significant (Fig. 7). As the number of Eulerian elements is

constant, they are also elongated significantly, and as stated before,

the accuracy of the results is strongly mesh dependent and re-

quires fine meshes. Therefore, the accuracy of the ALE model for se-vere deformations of the Eulerian box may be questionable

[75,129]. This mainly concerns the later part of the steady-flow re-

gime, though.

Fig. 6. Bird strike simulation on rigid plate with Eulerian impactor model.

Fig. 7. Bird strike simulation on rigid plate with ALE impactor model.



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5.3.2. Application of Eulerian model for bird strike simulations

The Eulerian approach was first used for bird strike simulations

in the late 1990s in [25,131] in the DYTRAN code. The authors com-

pared the results against PAM-CRASH results from a pure Lagrang-

ian simulation for the load cases of impacts on a fuselage panel and

an engine nacelle with quite similar results, but without error ter-

mination, which typically occurs in Lagrangian simulations due to

severe element distortion. Also in [38] and [132] the Eulerian ap-proach was used in DYTRAN for bird strike simulations (on rigid

and deformable plates and on a radome, respectively).

A classical Eulerian modeling approach in LS-DYNA with a fixed

Eulerian mesh was compared in [126] to the new ALE approach

with a moving Eulerian mesh. By translating, rotating and deform-

ing the multi-material mesh in a controlled way, the mass flux be-

tween elements could be minimized, which occurred to a higher

extent in the fixed Eulerian mesh. This could be shown in energy

plots, where the total energy of the system decreases much more

during the classical Eulerian bird strike simulation compared to

the ALE simulation. The number of elements could be kept smaller

than in a classical Eulerian model, increasing the efficiency.

In [87] the Lagrangian bird model was compared to a Eulerian

model in DYTRAN, with the Eulerian results correlating better to

test data. The Lagrangian model in general produced much higher

predicted impact loads, about two times higher than in the test

data.

The study in [109] compared Lagrangian and Eulerian bird imp-

actors in RADIOSS. Though both approaches correlated well with

experimental pressures, the calculation time with the Lagrangian

model was much higher due to the decreasing time step. In the

comparison study of [82], a tensile failure criterion for the Lagrang-

ian impactor was introduced, leading to significantly lower CPU

costs than the Eulerian model and was therefore preferred, since

the results were similar.

In [133] a Lagrangian model is compared to a Eulerian model in

LS-DYNA impacting a tail plane leading edge. The results differ to a

certain extent, as the Eulerian loading is less localized and more

spread, which is attributed to a too stiff representation of theLagrangian bird due to high element distortions.

Further examples for Eulerian bird strike simulations are found

in [128,134–137] for fan blade impact and in [138] for impact on

fuselage panels, in [139] on a cockpit bulkhead plate, in

[77,83,140–143] on a composite plate, in [144,145] on a wind-

shield, in [83,117,142,143,146,147] on a leading edge and in

[142] on a rotor spinner.

5.4. SPH bird impactor model

As a contrast to the Lagrangian and Eulerian soft body impactor

modeling approaches, where a regular finite element mesh is used,

different meshless particle methods were developed over the

years, aiming at the independence of mesh distortion problemsand computational efficiency.

Anghileri et al. [148,149] investigated a simplification of the

bird modeling in the early 2000s by describing the impactor using

only nodes with added lumped mass and initial velocity. This ap-

proach is inspired by the discrete element method (DEM). Contact

definitions apply the load onto the impacted structure. The advan-

tage, compared to a Lagrangian impactor model, is the reduction of

the CPU time by the factor 10 with no effect on the time step size

and the ability to easily cover severe deformations and splitting of

the impactor. The disadvantage of this method is the lack of inter-

nal interaction of the nodal masses that leads to the lack of dissipa-

tion mechanisms and hence to an unrealistic bird behavior [75].

Ref. [84] states that this lumped mass model exerts high frequency

force peaks, having a strong negative influence on local structuralresponse.

Further applications of particle methods are documented in

[18,20]. Spherical fluid elements with a centrally located node

were developed in the code WHAM for the impactor modeling in

a fan blade impact study. The spherical elements are assembled

in a closest-packed formation without structural connection, pro-

ducing the soft body impactor shape. Contact algorithms avoid

penetration of the elements and generate reaction forces. Another

particle method was proposed in the early 2000s in [19] based onthe DEM. The gelatin impactor is represented by spherical rigid

particles in conjunction with a visco-elastic–plastic penalty form

of Hertzian contact law. The parameters of this interaction law

therefore control the global fluid-like behavior of the projectile.

Promising results were obtained, although the spread of the bird

was slightly underpredicted.

Another particle method was initially developed and applied for

astrophysical problems in the 1970s: the SPH (Smoothed Particle

Hydrodynamics) method [150–153]. It caught attraction for the

splashing simulation of fluids and gained increased attention for

bird strike modeling in recent years.

5.4.1. Characteristics of SPH modeling

The SPH method is a meshless Lagrangian technique, based on

interpolation theory and smoothing kernel functions [154]. The

fluid is represented as a set of discrete interacting particles

(Fig. 4d), which are independent from each other, being able to

cover large deformations without the problem of mesh distortion.

Each particle has a mass, velocity and material law assigned to it,

which is not localized but smoothed in space by a smoothing ker-

nel function, typically based on a B-spline approximation [154–

156], defining the range of influence of the particle. Field variables

of an individual particle are computed through interpolation of the

neighboring particles, whereas a particle is considered a neighbor

when it is located within the smoothing length of another particle

[16]. As it is based on a Lagrangian technique, it can easily be

linked to conventional Lagrangian finite element models, avoiding

possible material interface problems associated with Euleriancodes [155].

Compared to the conventional solid Lagrangian mesh, where

the explicit time step decreases significantly with element defor-

mation, the time step is constant for the SPH model. However, a

sufficient particle density is required in order to achieve accurate

results, which may necessitate high memory resources and typi-

cally is a compromise between accuracy and required CPU time

[74,75]. The influence of the SPH mesh density was analyzed in de-

tail in [31,76,157], with the conclusion of a high influence on the

soft body pressure curve in impact simulations on a flat plate

(Fig. 8). Rössler [158] could also show that the time step has an

influence on the bird’s flow behavior and therefore on the pressure

curve.

In general, compared to the Eulerian model, the SPH method re-quires fewer elements, avoids the material interface problems

associated with it and normally has a shorter solution time [31].

The numerical robustness, compared to the conventional Lagrang-

ian mesh with its mesh distortion problems, is very high.

A disadvantage of the SPH method, as discussed in [75,159], is

the lack of sharp boundaries, which makes the application of

boundary conditions difficult and may also affect the definition

of fluid–structure interaction. The so-called tension instability is

identified as another weakness of the SPH method, which is re-

ferred to as the numerical collapse and unphysical clustering of

the particles under tension due to negative pressures [160–162].

Additional problems occur if the impacted area is not calibrated

but needs to be known for pressure calculations, because SPH par-

ticles do not have a foot print, hence the actual impact area re-mains undefined [182].



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5.4.2. Application of SPH model for bird strike simulations

The first adoption of the SPH method for bird strike simulations

is documented in the late 1990s and early 2000s [127,163,164],

where this approach was implemented in the code PLEXUS and

used for fan blade impact studies. The slicing of the bird could be

represented successfully. In a Lagrangian model like in [101], the

slices had to be predefined. In [165] not only the impactor, but also

the target plate were modeled with the SPH method, which re-

duced the global time step compared to a simulation with a

Lagrangian plate. Refs. [74,83,119,166–169,46,49,117,125,154–

156,158,170–183] used the SPH approach in LS-DYNA and PAM-

CRASH for bird strike investigations on leading edges and highlight

the increased stability, good potential of bird splitting and reduced

cost of the simulations compared to Lagrangian bird impactors.

SPH bird impactors for impact on fan blades are documented in

[105,137,167,184–186], for impact on engine nacelles in [187],

on a windscreen in [145,188], on composite plates in [83,158,174], on wing flaps in [5], on an aircraft radome in [189], on wing

pod and belly pod nose in [183] and on a helicopter rotor blade in

[190].

5.5. Comparison of different bird modeling methods

A large number of publications exist, where the most estab-

lished modeling approaches were compared for specific applica-

tions. A comparison against experimental data is also often given.

A benchmark comparison study was performed in [75,129],

comparing five modeling approaches in LS-DYNA: Lagrangian, clas-

sical Eulerian, ALE, SPH and the DEM-based nodal mass model. The

impact scenario was a 4 lb bird impact against a rigid target with

an impact angle of 30, experimental test data were available.The Lagrangian impactor model showed reliable results in absence

of large distortions, otherwise it led to high computational cost and

early error terminations. The ALE approach led to high costs com-

pared to the meshless methods and questionable results due to se-

vere deformation of the moving Eulerian box. Also for the classical

Eulerian model the numerical-experimental correlation was not

satisfying, which was expressed quantitatively with the highest

relative error in terms of impact force. The lumped mass model

provided poor results due to lack of internal interaction and unre-

alistic behaviour of the bird. The SPH method is the recommended

approach in this study, due to high stability, low cost and good cor-

relation with experimental observations in terms of scattering

particles.

In an extensive study in [76,157,191], Lagrangian, Eulerian andSPH impactors were compared in LS-DYNA in an impact study on a

flat plate, achieving consistent results within a range of 10% of

experimental reference data with slightly higher forces for the

Eulerian model. The Lagrangian method with element deletion

was found to be computationally more efficient than the SPH or

Eulerian technique. But still all three methods were recommended

by the authors. A similar study was performed by Chuan [192],

adopting the Lagrangian, Eulerian and SPH approaches in LS-DYNA

for impact simulations on flat plates. All models led to very similar

qualitative and quantitative results, although all being slightly

higher than the experimental reference pressure curves, which

was attributed to the assumptions made in the numerical model

(ideal rigid target plate, idealization of bird geometry, etc.). The

higher computational cost of the Eulerian approach was high-

lighted as well as the problems of bird splitting for the Lagrangian

bird. Lavoie et al. [31,32] performed a similar comparison study in

LS-DYNA for the Lagrangian, ALE and SPH bird impacting a rigid

plate. The Lagrangian bird was concluded to be worst due to theproblem of element distortion, having a very negative influence

on the pressure curve. Although element erosion was used and a

significant amount of the impactor mass was deleted, the compu-

tational time was 30 times higher than with the ALE or SPH model.

Both ALE and SPH results were found to be satisfying, with the SPH

model being slightly faster and easier to implement with fewer

parameters. Hachenberg et al. [88] also compared the three meth-

ods Lagrangian, Eulerian and SPH in LS-DYNA for bird strike simu-

lations on rigid plates and curved leading edges with respect to

qualitative deformation and splitting, contact forces and CPU time.

Due to mesh distortion problems, the Lagrangian models often led

to the highest CPU time and too low contact forces, while the Eule-

rian model and SPH led to consistent results, though being strongly

mesh dependent. Jenq et al. [79] used the Lagrangian, classicalEulerian and ALE approach in LS-DYNA for bird strike simulations

on a rigid plate. The Lagrangian impactor was found to be worst

due to severe mesh distortion, having an unrealistic pressure

curve. The classical Eulerian and ALE approaches both led to good

results with the ALE model being preferred due to slightly better

results and lower CPU cost.

McCallum and Constantinou [130] compared the Eulerian and

SPH approach in LS-DYNA for impact simulations on a square flat

aluminium plate fixed in translation and rotation at the outside

edges, leading to close agreement in the results of both approaches.

Similar qualitative results were obtained in the comparison study

of [128] with Eulerian and SPH models in LS-DYNA for impact sim-

ulations on a turbine engine. However, a certain loss of accuracy in

the Eulerian simulation due to dispersion and numerical leakage ishighlighted. Tho and Smith [142] compared ALE and SPH in

Fig. 8. Bird strike simulation on rigid plate with SPH impactor model.



10/20

LS-DYNA for impact simulations on rigid plates. Both techniques

produced a very similar shock wave and release pressure and that

correlate well with experimental pressure-time data. The steady-

state flow pressure was slightly overpredicted in the SPH model.

In following case studies on leading edges both approaches again

performed in a very similar and satisfying way in terms of bird

spreading and amount of damage. Similar conclusions were gained

in [36], where ALE and SPH models impacting a rigid plate werecompared in LS-DYNA. Both approaches were found to be useful

in terms of bird deformation behaviour, which was compared to

their high speed impact test videos. The deformations were slightly

better with the SPH approach but the pressure curves correlated

better to the experimental data with the ALE model.

Zammit et al. [137] also compared ALE and SPH models in LS-

DYNA in an extensive study. While the solutions for impacts on a

rigid plate where quite similar, various differences became appar-

ent for impact simulations on fan blades. The ALE model led to

higher internal energies and more damage to the fan blades. This

was mainly attributed to the fact that the ALE bird represents a

continuous medium that impacts the fan blade edge sooner as

the SPH bird, which represents particles with empty space be-

tween them. Consequently, the SPH simulation results also depend

on the positioning of the particles, which needs to be considered

for impact loads at different angles of attack. Furthermore, the time

step had to be reduced for the SPH model to avoid contact penetra-

tions, which led to higher computational cost compared to the ALE

model. Beyond that, the bird splitting behavior was similar for both

models.

Ryabov et al. [193] compared the Lagrangian, Eulerian and SPH

approach for fan blade impact simulations. The Eulerian approach

was not recommended by the authors because of high CPU cost

and inaccurate results. The Lagrangian and SPH models both led

to similar results with the Lagrangian approach being cheaper

and therefore recommended. Element erosion of the Lagrangian

impactor was used to avoid stability issues, which allows for a

small time step and therefore performance advantages. In a similar

study by Shmotin et al. [105] with Lagrangian and SPH bird modelsin fan blade impact simulations with LS-DYNA the SPH model was

found to correlate better to experimental results than the Lagrang-

ian model.

Guida et al. [78] analyzed Lagrangian and Eulerian bird models

in DYTRAN for the application of a bird strike on a wing leading

edge and found the Lagrangian model to be 10 times faster and

by far more accurate with respect to force peaks and extent of

damage in correlation with experiments. In contrast, the impact

simulations of Smojver and Ivancevic [147] on an aircraft wing flap

with ABAQUS showed that the Eulerian bird model is more stable

than the Lagrangian bird and the results appear to be physically

more realistic. Chandra et al. [83] compared the Lagrangian, ALE

and SPH technique for impact simulations on wing leading edges

with LS-DYNA and found a more widespread damage for the ALE

model. In contrast, the damage was more localized for the Lagrang-

ian and SPH models, resulting from higher peak forces and there-fore earlier element failure. The Lagrangian model was seen as

unfavorable due to high mesh distortion and erosive mass loss.

5.6. Summary on bird modeling methods

From this literature study it can be concluded that the three

most established bird modeling approaches (Lagrangian, Eulerian

and SPH) have their advantages and disadvantages and it often de-

pends on the specific application, software package, parameter set-

up, impactor geometry, mass and velocity, which approach is best

suited for the individual problem. However, a global trend is visi-

ble, that the Eulerian and SPH approaches are preferred today com-

pared to the Lagrangian modeling approach with its problem of

element distortion. Though, some recent studies still explore mod-ern Lagrangian approaches due to their accuracies and efficiency.

An overview of the advantages and disadvantages of these three

modeling methods is given in Table 1.

An overview of all bird strike simulation papers of this literature

survey is given in Table A1 in the appendix, sorted by the year of

publication. From this table it can be seen which software code

was used by the authors, which modeling approach has been

adopted, which impactor geometry, mass and velocity was selected

and which application was studied. Firstly, it can be seen that in

early publications the representation of the impactor by a pressure

load was dominating. Later, more and more Lagrangian, Eulerian

and SPH bird models were used. In most papers more than one ap-

proach for the bird modeling was used, in order to identify the best

approach for the given problem. Also a large scatter in impactorgeometries, densities and masses is visible, no uniformity could

yet be achieved in this discipline of bird strike analysis.

6. Impactor geometry for bird strike simulations

Although substitute bird impactors have been used for many

years in bird strike tests and simulations by a variety of organiza-

tions there is no standardized artificial bird shape. The geometries

Table 1

Overview of advantages and disadvantages of bird modeling methods.

Lagrangian model Eulerian model SPH model

Advantage + Simple model generation + No mesh distortion, constant timestep

+ No mesh distortion, constant time step

+ Low CPU time (before mesh distortion) + Numerically stable simulations + Numerically stable simulations

+ Impactor boundary clearly defined + Complex bird splitting can be

simulated

+ Complex bird splitting can be

simulated

+ Good representation of splashing

behavior

+ Good representation of splashing

behavior

+ Eulerian mesh motion (ALE)

reduces computational cost

+ Lower computational cost than

Eulerian model

Disadvantage – Severe mesh distortion leads to reduced time step, artificial

stiffening, loss of accuracy and error termination

– Model generation and results

visualization more complex

– Model generation more complex

– Hourglass problems – No clear outer boundary – No tensile behavior

– Element erosion may remove mass from the simulation – Numerical leakage: total energy

reduces with time

– No clear outer boundary

– Splashing behavior difficult to represent with Lagrangian

elements

– Fine Eulerian mesh necessary in

impact zone: expensive

– Higher CPU time than Lagrangian

model (before mesh distortion)

– Bird splitting difficult to cover – Relatively high computational

time



11/20

are typically chosen to reflect the principal mass and shape of the

torso of a real bird [130]. The four most established substitute bird

geometries are the cylinder, the cylinder with hemispherical ends,

the ellipsoid and the sphere (Fig. 9). The use of such a simple geom-

etry is also beneficial for an easy manufacturing. While the cylin-

drical shape of the impactor was preferred in early studies, it is

also clearly visible from Table A1 that the cylinder with hemi-

spherical ends is dominating today as the geometry for the substi-

tute gelatin bird. This results from the fact that the first

experimental studies by Barber and Wilbeck [21,23] were per-

formed with cylindrical projectiles and these tests were often ta-

ken as the basis for the numerical model development.

Numerous studies investigated the influence of the projectile

geometry. Nizampatnam [16] investigated the influence of the four

typical projectile shapes in Fig. 9 on the shock and steady-flow

pressure. Although all geometries showed rather similar results,

the cylinder with hemispherical ends in both cases was closest to

experimental data. In [86] both a cylindrical impactor and a cylin-

der with hemispherical ends were compared, with the latter geom-

etry considered as closer to a real bird. These two geometries were

also compared in [194,195] in an impact study on a windshield.

Again, a better correlation to actual bird strike test data were found

for the cylinder with hemispherical ends, which is also stated in

[74]. In older studies [25,107] the ellipsoid was preferred to the

right cylinder since sharp or regular shapes such as a cylinder pro-

duced unrealistic impact pressure profiles. In the study in [3,34]the three geometries right cylinder, cylinder with hemispherical

ends and ellipsoid were compared in a numerical study. A strong

influence especially on the shock pressure was observed, which

is highest for the straight-ended cylinder due to the largest instan-

taneous contact area. It was 43% higher than with the hemispher-

ical-ended cylinder, which in turn is 30% higher than with the

ellipsoidal projectile. The length-to-diameter aspect ratio of the

bird (1.5:1, 2:1, 2.5:1) was found to have little influence on the re-

sults. Increasing the bird mass from 4 to 6 and 8 lb also slightly in-

creased the pressure peak.

In contrast to these simplified bird geometries, the realistic

shape of a Canadian goose was represented by a multi-material

modeling approach based on biometric data in the study of McCal-

lum and Constantinou [130]. The long neck, torso and wings weremodeled with different densities using the SPH approach in LS-

DYNA, although still sharing the same material law. In a direct

comparison to the cylinder with hemispherical ends, also modeled

as an SPH impactor, significant differences in the load curve were

identified. Resulting from the initial neck impact, a noticeable plate

displacement was obtained before the main torso impacted the

target. Therefore, the authors concluded that the target panel is un-

der a state of pre-stress when the torso impacts, which may have a

significance on the final level of damage predicted for the struc-

ture. The study was yet extended by Nizampatnam[16] for an even

more realistic bird geometry modeling with SPH in LS-DYNA. The

head, neck, torso, bones, lungs and wings with different densities

and different equations of state were included in the model. The

individual peaks in the pressure–time diagram of head, torso, etc.could clearly be seen, also leading to a slightly different loading

scenario than with the simplified impactor. However, no experi-

mental data of a real bird with a forward neck and wings extracted

as simulated are available for comparison. Still, such studies ques-

tion the legitimacy of whether the chickens that are typically used

in bird strike certification tests are appropriate at all to represent

the bird strike incident during flight with a real bird with forward

facing head and extracted wings [29].

7. Bird impactor material models

Just like the heterogeneity of projectile shapes, numerous dif-

ferent approaches for the bird impactor material modeling can be

found in the various studies in the literature.

Generally speaking, real birds are mostly composed of water.

Therefore, a water-like hydrodynamic response can be considered

as a valid approximation for a constitutive model for bird strike

analyses [86]. Furthermore, the anatomic structure of birds in-

cludes several internal cavities like pneumatic bones, lungs and pe-

culiar air sacs, reducing the bird average density. In order to cover

the effects of these cavities in the numerical model, a homogenized

bird material with an average density between 900 and 950 kg/m3

after elimination of the feathers can be estimated [86,195]. This

corresponds to the void content of 10–15% in the porous gelatin

of an artificial bird, which is typically used for bird strike tests.

Nizampatnam [16] raises the point that in his study a higher poros-

ity of 30–40% gave better overall agreement to Wilbeck’s experi-

mental results than the typically used 10–15%. This study was

based on SPH bird impact simulations on an ideally rigid target,

where the material porosity was varied between 0% and 40%.

Several authors tried to model the bird with a simple elasto-

plastic material law with a defined failure strain [81,88,99,118],

and some of them highlighted the limitations of this simplified ap-

proach [95,113]. It is observed that no fluid-like flow response can

be achieved with such an elasto-plastic material law, only if the

shear modulus G is set very low [80]. In [11,93] even a rubber-like

hyperelastic Mooney–Rivlin material is applied to simulate the

bird behavior during impact. The determination of the material

constants is reported to be difficult and of key importance. How-

ever, besides an increase in computational efficiency, no compari-

son to results obtained with traditional bird models is given.It is much more common to use an equation of state (EOS) for

the constitutive modeling of the bird impactor, defining the pres-

sure–volume relationship with parameters of water at room tem-

perature. In most studies [3,7,32,35,47,77,79,139,141,142,146,

154,165,168,170,178,192,195,196] the polynomial form of the

EOS was used, where the pressure p is calculated by the following

equation:

p ¼ C 0 þ C 1l þ C 2l2 þ C 3l

3; ð4Þ

where C 0, C 1, C 2 and C 3 are material constants and l is a dimension-

less parameter based on the ratio of current density q to initial den-

sity q0:

l ¼

q

q0

1:

ð5Þ

Fig. 9. Different substitute bird impactor geometries.



12/20

In other studies [155,173,188] the simpler Murnaghan EOS was

used:

p ¼ p0 þ B q

q0

c 1

; ð6Þ

where p0 is a reference pressure and B and c are material constants.

A further approach, adopted in [104,105,129,184], is the Grüneisen

EOS:

p ¼ q

0C 2l 1 þ 1

c02

l a

2l2

1 ðs1 1Þl s2

l2

lþ1 s3

l3

lþ1

h i2 þ c0 þ alð ÞE ; ð7Þ

where E is the internal energy, c0 is the Grüneisen parameter and a,

C , s1, s2 and s3 are constants. However, in [16] it is recalled that the

Grüneisen EOS is only valid for solid materials that remain in the so-

lid state throughout the impact event and should therefore be used

with care for bird strike simulations.

Which EOS is used often depends on the individual software

code that is utilized, as most commercial codes are limited to

one or few of the abovementioned formulations. All EOS have in

common that certain material constants have to be defined, which

typically cannot be measured directly. A regular technique is to usesimplified analytical approximations or parameter calibrations in

reference simulations with comparisons to experimental data for

the parameter identification. This was performed in studies such

as [129] or [155] using an optimization software to determine

the parameters in conjunction with bird strike tests on instru-

mented plates.

8. Contact calculation in bird strike simulations

The fluid-structure interaction in a soft body impact simulation

like a bird strike is generally based on a contact algorithm, which

prevents penetrations and calculates reaction forces. From compu-

tational point of view, the contact algorithm plays a significant role

in the bird strike simulation, since it has to cope with large defor-mations and splitting of the projectile, sliding of the bird material

over the target surface and the creation of multiple contact inter-

faces due to possible fracture and penetration of the structure

[169]. An appropriate contact formulation is of great importance

as it significantly influences the pressure curve during impact sim-

ulations on a flat pressure plate [76]. Most contact algorithms in

explicit simulations are based on the penalty formulation, which

means that a certain penetration of the slave node (impactor) into

the master surface (target plate) occurs, before the respective reac-

tion forces as a function of the contact stiffness and penetration

depth are generated, pressing out the penetrating node. During

the flow regime of the projectile, significant oscillations in the con-

tact force can occur due to this penalty contact algorithm. Their

frequency and peaks depend on the penalty stiffness scale factor,which has to be selected with care for this contact pair with highly

different stiffnesses. Ryabov et al. [193] investigated numerous dif-

ferent contact types in Lagrangian bird strike simulations in LS-

DYNA and found them to have a strong influence on the results.

However, in most references, no detailed information on the con-

tact type that was used is given.

Shmotin et al. [105] investigated the influence of the friction

coefficient in the contact calculation between bird and metallic tar-

get structure with values from 0 to 1. Best results compared to

experimental results were obtained with zero friction.

A further important point is the contact area, where the pres-

sure is calculated for comparisons with experimental pressure

curves. In the reference test, the pressure transducer has a finite

size, which should be similar to the nodal area in the model, where

the nodal contact forces are evaluated and converted into a pres-

sure. Almost no paper addresses this topic. Only in a few studies

[46,156,158,170,174] the influence of selected areas of pressure

evaluation is analyzed. It could be shown that this area has a great

influence on the peak pressure, which is very high for a small area

and consequently lower with increasing area, as the stress peak in

the impact centre is smeared over a larger area.

9. Conclusions

During a bird strike on aircraft structures at the velocities of

interest, the bird behaves as a soft body and flows in a fluid-like

manner over the target structure, with the high deformations of

the spreading material being a major challenge for finite element

simulations. In an extensive literature survey the progress in bird

strike modeling over the last 30 years was assessed. The most

interesting conclusion is that no homogeneity or uniformity in

terms of a generally accepted modeling approach exists, neither

with respect to the discretisation method nor the material model,

contact formulation, impactor geometry, size or mass. This makes

such a literature overview especially valuable, as the global picturein terms of appropriate modeling techniques for bird strike simu-

lations is sometimes difficult to paint due to the high number of

different options.

First simple simulation models in the 1970s and 1980s mainly

used nodal pressure loads to represent the bird impact load. They

were replaced by Lagrangian impactor models in the following

years. However, the main problem in using a Lagrangian impactor

model is the mesh distortion due to the large spreading of the

material, which causes time step and stability problems and the

difficulty in modeling splitting of the bird. Therefore, more suitable

methods for the simulation of fluid-like flow behavior like the

Eulerian or meshless SPH technique were adopted in recent years.

However, none of these approaches is free of disadvantages, which

is the main reason why none of the methods has established as thestandard modeling technique until today. It often depends on the

specific application, software package and parameter setup to

determine which approach is best suited for the individual prob-

lem. The best solution for one case may just be the second best op-

tion for another case. It is therefore common practice to adopt

different modeling methods and to assess through validation,

which approach is most beneficial for a given problem. Generally

speaking, a trend is visible towards the utilization of Eulerian or

SPH models with an equation of state for the impactor material

using the properties of a water–air-mixture at room temperature.

Very good correlation to experimental results could be obtained

with these models.

Although the certification of bird-proof aircraft components to-

day still depends on real physical tests, proposals are increasinglyput forward to use more simulation techniques instead of experi-

ments during certification in certain well-defined scenarios. In this

context, it would be desirable to increase the uniformity and com-

parability of bird strike analyses, e.g. in terms of projectile geome-

try, mass and composition, which was encouraged by many

authorities before but has not been achieved yet. Also the general

availability of reliable up-to-date test data for common bird impac-

tor model validations is desirable for future bird strike analyses.

Appendix A

Table A1.



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Table A1

Survey of bird strike simulation papers and modeling data in technical literature.


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T a b l e

A 1

( c o n t i n u e d )



15/20

( c o n t i n u e d

o n

n e x t p a g e )



16/20

T a b l e A 1

( c o n t i n u e d )



17/20

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