Arbitrary Lagrange Eulerian Approach for Bird-Strike Analysis Using LS-DYNA

2013 American Transactions on Engineering & Applied Sciences.

American Transactions on
Engineering & Applied Sciences
http://TuEngr.com/ATEAS

Arbitrary Lagrange Eulerian Approach for
BirdStrike Analysis Using LSDYNA
Vijay K. Goyal
a
b

a*

a

, Carlos A. Huertas , Thomas J. Vasko

b

Department of Mechanical Engineering, University of Puerto Rico at Mayagüez, PR 00680 USA
Engineering Department, Central Connecticut State University, New Britain, CT 06050 USA

ARTICLEINFO

A B S T RA C T

Article history:
Received December 23, 2012
Received in revised form
26 February 2013
Accepted March 01, 2013
Available online
March 08, 2013

In this third and last sequence paper we focus on developing
a model to simulate bird-strike events using Lagrange and Arbitrary
Lagrange Eulerian (ALE) in LS-DYNA. We developed a standard
work for the two-and three-dimensional models for bird-strike
events. We modeled the bird as a cylinder ﬂuid and the fan blade as a
plate. The case study was that of frontal impact of soft-bodies on
rigid plates based on the Lagrangian Bird Model.
Results show
very good agreement with available test data and within 7% error
when compared with the Lagrange and SPH methods. The
developed ALE approach is suitable for bird-strike events in tapered
plates.

Keywords:
Finite element;
Impact analysis;
Bird-strike;
Arbitrary Lagrange-Eulerian.

2013 Am. Trans. Eng. Appl. Sci.

1. Introduction
As we mentioned in previous two papers, the collisions between a bird and an aircraft are
known as a bird-strike events. With modern computer capabilities, we can try to simulate
bird-strike events and predict the damage to engine components [1–3]. Typically, we use the
Lagrangian method because it is easy to model such events. However, with new methods in the
* Corresponding author (V. Goyal), Tel.: 1-787-832-4040 ext. 2111; E-mail:
2013. American Transactions on Engineering & Applied Sciences.
vijay.goyal@upr.edu.
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horizon such as Arbitrary Lagrangian Eulerian (ALE), the question is how promising are these new
methods.
When we model the bird and fan blades using the Lagrangian description, we encounter that
there is a loss of bird mass due to the fluid behavior of the bird, which causes large distortions in the
bird model. This loss of mass may reduce the real loads applied to the fan blade, which is the real
motivation to use the Arbitrary Lagrangian Eulerian [4–8] (ALE) in this work. LS-DYNA has
integrated the ALE formulation to model this fluid-structure interaction problem but the bird-strike
events have not been fully studies using this computational tool.
In the Lagrangian model, the numerical mesh moves and distorts with the physical material,
allowing accurate and efficient tracking of material interfaces and the incorporation of complex
material models. One disadvantage of this method is the negative volume error, which occurs as a
result of mesh tangling do to its sensitivity to distortion, resulting in small time steps and
sometimes loss of accuracy.
The simulations of the ALE bird-strike event performed in this work include only two
dimensional cases. The good results in two dimensional ALE simulation of a bird-strike may be
obtained by inputting into our analysis the parameters used by Souli and Olovsson [6]. The
geometrical properties of their work may not match the ones found used here, but the differences
are insignificant. The material properties for the plate have been varied along with the initial
velocity of the void/bird part and the constraints present in the SPC card for the target. The force
plots obtained resemble those generated during the ALE and Lagrangian simulations.

2. Background and Motivation
Barber et al. [9] found that bird impacts in rigid targets generated peak pressures independent
of bird size and proportional to the square of the impact velocity, resulting in a fluid-like response.
Barber et al. presented the time-dependent pressure plots for the impact of birds against a rigid
cylindrical wall. This work was taken as reference to create simulations similar to those presented
by Barber et al. [9].
The MacNeal-Schwendler Co. [8] showed that the ALE description of a bird-strike against a
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Vijay K. Goyal, Carlos A. Huertas, and Thomas J. Vasko

leading edge is able to simulate and predict the leading edge cusp (deflection). They compared the
results using the ALE description with those of the Lagrangian description and the test data. For the
Lagrangian and ALE solution, results and CPU time were shown. For the contact algorithm, it
was not necessary to use an eroding contact algorithm but a regular Master-Slave contact for panel
bird interaction. The analysis of the Lagrangian technique took a CPU time of 1.7 hours using SGI
R8000 port of MSC/DYTRAN.
The work performed by Moffat et al. [10] was used to reproduce models of impact of birds on
tapered plates. Moffat et al. [10] worked in the use of an ALE description of bird-strike event to
predict the impact pressures and damage in the target plate. This work used the MSC/DYTRAN
code for the simulations instead of LS-DYNA which is the code used in this project. The article
presents some previous work involving rigid plate impacts from Barber et al. [9] and a flexible
tapered plate impacts from Bertke et al. [11]. These two kinds of impacts were reproduced in the
work by Moffat et al. [10] using the finite element description in MSC/DYTRAN. The geometrical
model that was used for the bird was a cylinder with spherical ends with an overall length of 15.24
cm and a diameter of 7.62 cm. The bird density is 950 kg/m3. Moffat et al. [10] found that the
pressures were insensitive to the strength of the bird and a yield stress of 3.45 MPa was taken for
the rigid plate impact analysis. For the viscosity it was necessary to take higher values for impacts
at 25°. The article shows plots of the shock pressures for different velocities and for different bird
sizes. For the tapered plate impact simulation a 7.62 × 22.86 cm plate was used. The plate was
tapered by 4° and the edge thickness was 0.051 cm which blended to 0.160 cm for the majority of
the plate. The work did not specify the kind of element that was used for the tapered plate. For
the LS-DYNA simulation performed in this research the tapered plate will be simulated using shell
elements.
In the case of the ALE formulation an Eulerian material with shear strength was chosen with a
third order polynomial equation of state. The tension cutoff was the same as in the Lagrangian
technique. For the contact algorithm an ALE fluid-structure coupling algorithm was used and an
Eulerian mesh had to be created. The bird that was modeled as an Euler fluid flows thru the
Eulerian mesh. The results showed the same variables as in the Lagrangian model. The time used
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for the CPU on SGI R8000 port was one hour. The results obtained with the Lagrange model and
the ALE models were very close to the test data although the ALE simulation employed less CPU
time for the analysis stage.

In addition the ALE simulation gave more accurate physical

description of bird slicing and breakup.
After a careful review, very little work was found using ALE formulation to model bird-strike
events. Thus, we developed a standard work for bird-strike events using the ALE method. We
compared the results by those obtained using the Lagrangian formulation [12] and Smooth Particle
Hydrodynamic formulation [13].

3. Impact Analysis
We considered the bird at impact as a fluid material. The soft body impact results in damage
over a larger area if compared with ballistic impacts. Now, to better understand, bird-strike events
let us first understand the impact problem and then apply it to the bird-strike event being studied in
this work.

3.1 A Continuum Approach
Three major equations are solved by LS-DYNA to obtain the velocity, density, and pressure of
the fluid for a specific position and time. These equations are conservation of mass, conservation
of momentum, and constitutive relationship of the material Cassenti [14]. The conservation of
momentum can be stated as follows:

(1)
where P is a diagonal matrix containing only normal pressure components, ρ the density, and V the
velocity vector. The second equation used in the analysis is the conservation of mass and it is
written as per unit volume as follows:

(2)
We can further express constitutive relation in its general form as follows:
(3)

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3.2 ALE Approach
The Lagrangian method uses material coordinates (also known as Lagrangian coordinates) as the
reference. The major advantage of the Lagrangian formulation is that the imposition of boundary
conditions is simpliﬁed since the boundary nodes are always coincident with the material
boundary. Each individual node of the mesh follows the associated material particle during
motion.

This allows easy tracking of free surfaces, interfaces between materials and

history-dependant relations. The major disadvantage of this method is that large deformations of
the material lead to large distortions and possible entanglement of the mesh. Since in the
Lagrangian formulation the material moves with the mesh, if the material suffers large
deformations, the mesh will also suffer equal deformation and this leads to inaccurate results.
These mesh deformations cause inaccuracy in the simulation results. To correct this problem,
remeshing must be performed which requires extra time.

Figure 1: Description of motion for Lagrange formulation.
The reference coordinates for the Lagrange method are the material coordinates (X). Let us
deﬁne RM as the material domain (reference for the Lagrangian domain) and RS as the spatial
domain. The motion description for the Lagrangian formulation is:

(4)
where

is the mapping between the current position and the initial position, as shown in

Figure 1. The displacement u of a material point is defined as the difference between the current
position and the initial position:

(5)
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Figure 2: Lagrange, Eulerian, ALE Methods.

Figure 3: Maps between material, spatial and referential domains.
The ALE formulation [15] is a combination of the Lagrangian and Eulerian methods. In this
method the reference coordinate is arbitrary and is generally presented as χ. Depending on the
motion, the calculations are Lagrangian based (nodes move with the material) or Eulerian (nodes
ﬁxed and the material moves through the mesh). The user must specify the optimal mesh motion,
which is the major disadvantage of the ALE method. Figure 2 presents the differences between
the mesh motions in the Lagrangian, Eulerian and ALE formulations.
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In the ALE method, the referential domain is denoted as RR and the reference coordinates are
denoted as χ. The position of the particle may be defined as

, and the mesh motion

. The mesh displacement is defined as

as

(6)
The relationship between material coordinates and ALE coordinates, as shown in Figure 3, is
given by
(7)
where,

by composition of functions.

For the Lagrange mesh, the nodes are assigned to material particles; therefore the mesh motion
is equal to the material motion. On the other hand, the nodes in the Eulerian mesh are fixed and the
material flows through the mesh. The ALE formulation is a combination of the Lagrange and
Eulerian, therefore the nodes can be fixed (as in the Eulerian mesh) or moving with the material
(Lagrangian mesh).
Table 1: Comparison of peak pressure for different Lagrange, SPH and ALE simulations.

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Figure 4: Beam impact problem.

4. Beam Centered Impact Problem
Before studying bird-strike events, we proceeded to solve a beam centered impact problem
[12]. The problem consisted in taking a simply supported beam of length, L, of 100 mm over
which a rigid object of mass, mA, of 2.233 × 10−3 kg impacts at a constant initial velocity of, (vA)
1,100 m/s. The beam has a solid squared cross section of length 4 mm, modulus of elasticity, EB,
of 205 GPa, and a density, ρB, of 3.925 kg/m3. Figure 4 shows a schematic of the problem. The
goal of this problem is to obtain the pressure maximum peak pressure exerted at the moment of
impact. The problem is solved analytically and then compared to the corresponding outputs from
LS-DYNA for the Lagrange method (Table 1).

4.1 Analytical Solution
Since the impact occurs at only one point, the problem can be solved by concentrating all the
mass of the beam at the point of impact, i.e., at the center of the beam. Thus will simply the
problem to a problem of central impact between two masses, as shown in Figure 5.

Figure 5: Beam impact problem simplification.
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The impulsive time-average constant force

acting during the time of the impact is found

as [12]:

(8)
where ∆ is the time it takes to complete the impact. Equation (8) has two unknowns: the
average force and the impact time. The impact time is taken to match the impact time given by
LS-DYNA, and thus performs a fair comparison. Once the impact time is known, the force is
obtained straight forward using Equation (8).

4.2 ALE Simulation
We solved this problem using the Arbitrary Lagrange Eulerian (ALE) description. The major
challenge in this ALE model was that LS-DYNA does not allow the use of rigid material for the
bird and the creation of a reference void mesh around it. As discussed earlier the constitutive
relation for this material varies from that used in the Lagrange case [12].

Figure 6: ALE simulation of transversal beam impact.
Figure 6 shows the progression and the deformation obtained in this simulation. The impulse
time for this simulation was similar to that obtained using Lagrangian approach and was ∆ = 8.10
µs. Using Eq. 8, the analytical impact force was 27.58 kN. The analytical impact force was
27.65 kN and the peak pressure as 1.105 GPa. The peak force in this ALE simulation was 25.94
kN which is 6.2% lower than the analytical value. The pressure from the ALE method is
calculated as 1.037 GPa. The values obtained with the ALE model are within 6% with those
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obtained using the Lagrangian model.

5. BirdStrike Impact Problem
Barber et al. [9] performed an experimental characterization of bird-strike events and it was
our interest to use the ALE formulation in LS-DYNA to analyze bird-strike against flat and tapered
plates. We use the work by Barber et al. [9] as a mean of comparison. The results within 10%
would be acceptable since the actual testing model is not available.
In order to achieve a fair comparison with the Lagrange, SPH simulations and the test data, we
kept the same bird properties as in the Lagrangian case [12,13]. Two different simulations were
performed: 2D and 3D. The first one is a 2D simulation based on the work done by Souli and
Olovsson [6], which has been proven to yield acceptable results. The second model is a 3D
simulation trying to reproduce the bird strike event in solid rigid plates studied by Barber et al. [9].
Also, a 2D version of this test is created. All computer simulations generated data that are
compared with the experimental work and the Lagrangian case of the same bird-strike event.
Table 2: Bird model used for the ALE simulation.

5.1 BirdModel
The bird model establishes the most important variables and parameters that better fit to high
speed bird-strike events when simulated with computer software. The ALE bird model uses
parameters given in Table 2.
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5.2 Bird Impact against a Flat Plate
Here we used two different targets: a rigid flat plate and a deformable tapered plate. The
purpose of using a rigid flat plate target is to compare the simulations with the experimental data
obtained from Barber et al. [9]. Barber et al. [9] used a rigid flat plate for their experiments which
was modeled as a circular rigid plate with dimensions of 1 mm thickness and 15.25 cm of diameter.
The material of the target disk was 4340 steel, with a yield strength of 1035 MPa, Rockwell
surface hardness of C45, modulus of elasticity modulus of 205 GPa, and a Poisson’s ratio of 0.29.
These properties of the material will be used in LS-DYNA to model the flat rigid plate. The birds
used in the tests weigh about 100 grams and are fired at velocities ranging from 60 to 350 m/s. To
achieve a better simulation of the bird-strike event the densities of the computer simulated bird
must be calculated based on the masses of the tests and the recommended bird cylinder-like
computer model. The target disk must be modeled as a circular rigid plate.

Figure 7: Geometric model for the Lagrangian bird and target shell.

Figure 8: Deformation of the shell target in the ALE description.
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The computer simulations are based on the data given by the Barber et al.[9] research and the
bird model used. The purpose of these simulations is to compare analytical results (computer
simulations) obtained by using the ALE method with experimental results and the current
Lagrange model. LS-DYNA data output parameters such as *DATABASE_RCFORCwere used to
obtain the impact force.
5.2.1 Bird Strike Simulation Using 2D ALE
Let us begin with the 2D ALE model. First, we varied the coupling and reference system
parameters

inside

the

*CONSTRAINT_LAGRANGE_IN_SOLIDand

*ALE_REFERENCE_SYSTEM_GROUP cards. By studying the deformations, the best results
are achieved when we take a reference system type parameter of PRTYPE=5 and a coupling type
parameter of CTYPE=5.
Here, we set the initial velocity of the model to 198 m/s (442.9 mph), which is the velocity
used in the Lagrange simulation [12]. This velocity is assigned to a node set containing the bird
and the void mesh using the *INITIAL_VELOCITY card. A moving mesh was simulated without
constraints of expansion. The material used for the target was the *MAT_PLASTIC_KINEMATIC
and for the bird and void the *MAT_ELASTIC_FLUID. A penalty coupling was used to specify
the type of coupling inside the *CONSTRAINED _LAGRANGE_IN_SOLID card. Figure 8
shows the interaction between the bird and the shell and the moving reference for the void mesh.
The void has no constraints of rotation about the z–axis.
The impacting progression for this simulation can be observed in Figure 8. It can be observed
that the modeled bird deforms to the sides although there is no a complete sliding of all of the bird
material on the target. The mesh deforms as the bird impacts the target. The reference system
follows an automatic mesh motion following a mass weighted average velocity in ALE. The
maximum pressure obtained in this.
ALE simulation is approximately 3.5 MPa. The model used in this simulation has smaller
dimensions than the dimensions of the bird tested by Barber in shot 5126A and for this reason it
was not expected to produce the same results as in the test data. However, the behavior of the
pressure between the ﬂuid and the structure is similar to that observed in both Lagrange simulations
and experimental data by Barber et al. [9]. Once again, the steady state for this case is not as well
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captured; instead the zero value is obtained after a short period of time.
The maximum force obtained for this ALE simulation is 0.080 MN in the negative x direction.
This result can not be compared with the Lagrange simulation because the geometrical models in
both cases are not the same. The variables used in the ALE cards for this case will be used as
reference to create an ALE model that fits the geometrical dimensions of a bird strike performed by
Barber et al., specifically shot 5126 A.
5.2.2 2D ALE Simulation of Shot 5126A
By changing various bird parameters, a new deformation for the model bird is created. The
deformation is shown in Figure 9. The reference system composed by the surrounding void mesh
translates following an automatic mesh motion using mass weighted average velocity. The
NADV variable (Number of cycles between advection) was changed to the flag of 1 in the
*CONTROL ALE card.

Figure 9: Deformation of the 2D ALE bird impacting a rigid plate.
The peak pressure is approximately 36 MPa, which is 10% lower than the 40 MPa measured
by Barber et al. [9] and 17.54% lower than the 43.66 MPa obtained from the Lagrangian
formulation using the elastic fluid material. In this case there is almost no variation in the impact
area when compared with the SPH and Lagrange methods. Also, in the ALE method there is no
change in the global mass of the model as in the Lagrange method. Hence, there was no change in
the mass, in contrast with the Lagrange model. This suggests that the loads generated with the
ALE method would be more accurate to the real loads generated in a bird-strike event. This also is
supported by the fact that the peak pressure obtained in the ALE method was 10% of the test data
obtained by Barber et al [9].
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Figure 10: Pressure contours for the ALE simulation using NADV=1.
Figure 10 shows the pressure contour progression for this simulation at different times of the
impact. The fringe levels changes from one plot to another in different time intervals. As
observed in this ﬁgure, a shock pressure is generated at the moment of the impact. This shock
pressure travels from the front to the back of the simulated ALE bird. The highest value obtained
was 278 MPa. This is the pressure calculated for one ALE element inside of the modeled bird and
does not necessarily represent the pressure exerted on the target. The pressure contours also
confirm that the compressive shock waves, shown by Cassenti [14], are also calculated by the 2D
ALE simulation of a bird-strike.

Figure 11: Meshing of the ALE simulation of Shot 5126.
5.2.3 Bird Strike Simulation Using ALE in 3D
A three dimensional ALE model in LS-DYNA of shot 5126A Barber et al. is also created.
The simulation is performed by creating a void mesh inside of the bird. The dimensions and
parameters were those corresponding to shot 5126 A. The material used for the bird was the
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*MAT_ELASTIC_FLUID and *MAT_PLASTIC_KINEMATIC for the plate. The formulation
used for the ALE bird and surrounding void mesh simulation was the one-point integration with
single material and void.
Figure 11 shows the meshing of the void material for this simulation. Also the merged nodes
on the common boundaries of the void and the cylinder can be observed. This is a necessary
condition to allow the bird material to flow through the void mesh. The number of cycles between
advection (NADV) variable inside the *CONTROL_ALE was set to one.

The continuum

treatment used for this simulation was DCT = 2 (EULERIAN). The void mesh and bird moved
together with an initial velocity of 198 m/s (442.9 mph) against the rigid flat plate.

The

deformation of the bird and void mesh started when the ALE bird impacts the Lagrangian target.
The penalty coupling was used to define the coupling. This means that the forces will be
computed as a function of the penetration of the bird in the target.
5.2.4 Variation of the Coupling Type
Changes in the type of coupling used in the ALE model were performed in order to study the
influence of this variable in the pressure calculated by LS-DYNA for the bird-strike simulation.
The

coupling

type

variable

(CTYPE)

is

included

in

the

*CONSTRAINED_LAGRANGE_IN_SOLID card.
Using Acceleration Constraint Coupling
For this case the type of coupling used was an acceleration constraint or CTYPE=1. This
coupling was used to calculate the forces between the Lagrangian target and the ALE bird.
Although we observed a deformation of the plate after the impact, no pressure was calculated when
using acceleration constraint. The simulated ALE bird went through the flat plate without
deformation. Therefore this type of coupling is not recommended for bird-strike modeling.
Using Constrained Acceleration Velocity
The next coupling used is the constrained acceleration velocity that is the default value used by
LS-DYNA (CTYPE=2). We observed that no pressure was computed for the fluid-structure
database. Therefore, this coupling type does not produce good results for this type of problems.
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Using Constrained Acceleration Velocity in the Normal direction
For this simulation the coupling type used was an acceleration velocity constraint in normal
direction only (CTYPE=3) for the coupling between the ALE bird and the Lagrangian target. No
pressure was observed.

Figure 12: Average pressure for the 3D ALE simulation of the bird-strike.
Using Penalty Coupling without Erosion
The next coupling type used was the penalty coupling (CTYPE=4). The final shape of the
deformed bird for this case encloses the same behavior to that obtained in the 2D ALE simulation.
The deformation for this simulation was not as accurate as desired and as a consequence the
pressure in the coupling interface registered an approximate value of 95 MPa as seen in Figure 12.
This value is 135% higher than the 40 MPa measured in the test data corresponding to shot 5126A
from Barber et al. [9] and 117% higher to the 43.6 MPa of the Lagrangian case. The reason is that
the equation of state is a function of time and thus the time step scale factor (TSSFAC) needs to be
changed.
5.2.5 Variation of the Time Step Scale Factor
The Time Step Scale Factor (TSSFAC) inside the *CONTROL_TIMESTEP was modified in
order to change the time step used for the ALE calculations. It is desired to study how this
variation affects the final results in the time history force and pressure generated by the fluid
structure database output.
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Figure 13: Average pressure for the 3D ALE simulation
of the bird-strike with change in TSSFAC.
Table 3: Comparison of peak forces for different Lagrange, SPH and ALE tapered plate impact
simulations at 0 degrees.

The TSSFAC used in the previous 3D ALE simulation was 0.35 which produced a peak
pressure of 95 MPa, as seen in Figure 12. A value of TSSFAC of 0.58 produced similar
deformation however the pressure plot changed.

The new peak pressure obtained in this

simulation that was 44.85 MPa 12.25% higher than the experimental value of 40 MPa found by
Barber et al [9]. Another value used was a TSSFAC of 0.90. The deformation obtained again
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was similar to previous 3D ALE simulation. The peak pressure for this case is 19.4 MPa, which is
51.4% lower than the experimental value. When the TSSFAC was set to 0.58 the peak pressure
obtained was 44.85 MPa which is 12.12% higher than the experimental value of Barber. Figure
13 shows the influence of the time step scale factor on the maximum peak pressure at the impact
time. The optimum value that for which a steady value is maintained. Thus a value of 0.58 is
selected.
Table 3 shows the comparison of the average peak pressure generated for each of the ALE
simulation with the test data from Barber et al. [9]. As observed when the TSSFAC is increased
from the original value of 0.35 it considerably decrease the error compared with the test data. The
optimum value of the pressure in which the error was the lowest possible, 12%, was obtained when
the TSSFAC was 0.58. Therefore, it can be concluded that for simulation of bird-strike using the
ALE method in 3D a value of 0.58 should be used for the TSSFAC. The error for the Lagrange
and SPH simulations are under 10% and for the 3D ALE simulation with TSSFAC the error
obtained was 12%. The material used for the Lagrange and ALE is the elastic ﬂuid and for the
SPH was material null. The peak pressure using the 2D ALE case has a delay which is irrelevant
because it only depends on the time that takes the bird to impact the plate which is a function of the
distance in which the bird was placed initially.

6. Tapered Plate Impact at 0 Degrees
Now, we model a bird striking a tapered plate as was in the case of the Lagrangian model and
SPH model. The bird properties and the tapered plate are taken as the used by Moffat et al. [10].
Two different impact angles for tapered plate are considered: 0 degrees and 30 degrees. The
material used for the bird model is *MAT_ELASTIC_FLUID with a penalty coupling. The
variables for the *REFERENCE_SYSTEM_GROUP were kept the same as in previous
simulations.
First a 2D simulation of the impact of the bird against the tapered plate was performed. The
coupling of the bird and the tapered plate needs to be calculated in all the directions. This can be
obtained

setting

the

value

of

the

DIREC

variable

inside

the

*CONSTRAINT_LAGRANGE_IN_SOLID to 3. The type of coupling used in this simulation
was the penalty coupling (CTYPE=4). The peak force obtained was 0.01461 MN with an error of
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1.4% if compared with the Lagrangian simulation of the same case. It can be observed that the
bird did not go through the plate.

Figure 14: ALE Bird impacting a tapered plate at 0 degrees at different time intervals and the top
view of the tapered plate after the impact.
Table 4: Comparison of peak forces for different Lagrange, SPH and ALE tapered plate impact
simulations at 30 degrees.

The results obtained in the ALE simulation of a bird-strike impact against a tapered plate at 0
degrees were similar to that of the Lagrange and SPH cases. Figure 5.22 shows the interaction of
the bird and the plate. As expected, the bird was sliced in two parts and the plate was slightly
deformed as seen in Figure 14. However, the pressure plot generated by the *DATABASE_FSI
shows that there were little interaction between the Lagrangian plate and the ALE bird. It was
necessary to vary the penalty factor in this simulation in order to calibrate the value of the force
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calculated in the coupling. The penalty factor (PFAC) is used only when a penalty coupling type
is included in the keyword. The PFAC variable scales the estimated stiffness of the interacting
(coupling) system. A value of 860 was used in our case which was found to be the optimum value.
The maximum value of the average pressure was 0.0112 MN, 20.4% lower than the 0.0141 MN
computed by the Lagrange case using material elastic fluid.
The comparison for the peak force and the maximum normal deﬂection obtained in the
simulations of the impact of a bird against a tapered plate using Lagrange, SPH and ALE
formulations are shown in Table 4.

Figure 15: ALE Bird impacting a tapered plate at 30 degrees at different time intervals and the top
view of the tapered plate after the impact.
6.1

Tapered Plate Impact at 30 Degrees
The maximum deflection for this case was measured to be 1.18 in, 11.9% higher than the value

obtained by Moffat et al. [10]. The maximum force obtained in this simulation was 0.05319 MN
which is 6.06% higher than the Lagrange case. This value was obtained using a penalty coupling
with a penalty factor of 120.
The 3D simulation of the bird impact at 30 degrees against the deformable tapered plate
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showed that the deformation in the ALE simulation has a similar behavior as in the Lagrangian
case [12]. The maximum normal deflection shown in Figure 14 for this ALE simulation was 1.25
in which is 19.8% higher than the value found by Moffat et al. [10] and 5.65% lower than the
Lagrange case using elastic fluid material. In addition, the ALE bird suffered a little change in
dimensions only without any loss of mass.
The peak force obtained in the ALE simulation was about 0.04761 MN, 15.9% lower than
0.0566 MN obtained in the Lagrange simulation [12]. For this simulation also was necessary to
calibrate the value of the penalty factor PFAC to a value of 170, which was the optimum value.
As previously stated, the main reason for the difference is the type of material used in the ALE
method. Another reason for this could be that in the ALE simulation the bird did not presented
any loss of mass as in the Lagrangian case. Also, the SPH formulation [13] the particles of the
modeled SPH bird interact in the impact, which could be one of the causes of the low force
obtained. The difference in the time in which the peak pressure occurs for each case is irrelevant
because the time parameters and the distance from the initial position of the bird to the target were
different for each formulation.
The comparison for the peak force and the maximum normal deflection obtained in the
simulations of the impact of a bird against a tapered plate using Lagrange, SPH and, ALE
formulations are shown in Table 4.

7. Final Remarks
The three computational methods (Lagrangian, SPH and ALE) used in LS-DYNA have shown
to be robust for the one-dimensional beam centered impact problem. The peak pressure from all
three cases has an error smaller than 7% when compared to the analytical results. For the
Lagrangian and SPH the error is less than 5%. Thus, the three methods can be used to study
soft-body impact problems, such as bird-strike events. For the frontal bird-strike impact against a
flat rigid plate, the best contact was the eroding contact type and the best Lagrangian material was
material elastic fluid, which is a material specialized to model a fluid-like behavior taking in
consideration the deviatoric stresses which are not considered for the null material. The Lagrangian
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129

simulations show that the results are in within 10% when compared to already available
experimental data in the literature. The 2D ALE simulation, using an automatic mesh motion
following a mass weighted average velocity and a penalty coupling produced a peak pressure of 36
MPa, and the results were within 10% with the pressure measured by Barber et al. [9]. The peak
pressure using the 3D ALE simulations showed sensibility to the time-step scale factor (TSSFAC).
It was shown that the best time scaled parameter is that of TSSFAC=0.58 which produces an error
of 12.12% when compared with that by Barber et al. [9]. Both Lagrangian and ALE models used
the material elastic fluid which can explain the convergence in their results. For flat plate impact
simulation using a SPH bird constructed using two different mesh resolutions, if the contact
*CONTACT_CONSTRAINT_NODE_TO_SURFACE the pressure obtained is 37.3 MPa with an
error of 6.75% over the test data. Therefore, it is recommended to use the above type of contact
when studying SPH bird-strike events against rigid flat plate impacts simulations because it better
represents the deformations and pressure obtained with the test data.
For the 0 degree bird impact against a tapered plate, there was a small ﬂuid-structure
interaction because the bird is basically sliced in two parts. This behavior is observed by all three
approaches. For the 30 degrees bird impact against a tapered plate, the Lagrangian and SPH
produce peak forces within 10% error and the maximum normal deflection are found within 13.3%
when compared to the maximum normal deflection found by Moffat. However, the maximum
normal deflection found in this ALE simulation was 1.25 in, 19.73% higher than the value found by
Moffat et al. [10]. Therefore, based on these simulations the ALE approach can be used for
bird-strike events in tapered plates.

8. Acknowledgments
This work was performed under the grant number 24108 from the United Technologies Co.,
Pratt & Whitney. The authors gratefully acknowledge the grant monitors for providing the
necessary computational resources. The research presented herein is an extension of the work
presented at the 47th AIAA/ASME/ACE/AHS/ASC SDM Conference, Rhode Island, May 2006,
AIAA-2006-1759.

130


9. References
[1]

T. Vasko, “Fan Blade Bird-Strike Analysis and Design”, Proceedings 2000 of the 6th
International LS-DYNA Users Conference, 2000. Detroit, USA, pp.(9-13)–(9-18).
http://www.dynalook.com/international-conf-2000/session9-2.pdf Accessed December
2012.

[2]

C. Shultz, J. Peters, Bird Strike Simulation Using ANSYS LS/DYNA. 2002 ANSYS users
conference. Pittsburgh, PA, 2002.

[3]

J. Metrisin, B. Potter, Simulating Bird Strike Damage in Jet Engines, ANSYS Solutions 3
(4) (2001) 8–9.

[4]

C. Linder, “An Arbitrary Lagrangian-Eulerian Finite Element Formulation for Dynamics
and Finite Strain Plasticity Models”, Master’s thesis, Department of Structural Mechanics,
University
Stuttgart,
Stuttgart
(2003).
115p.
Accessed
http://www.ibb.uni-stuttgart.de/publikationen/fulltext/2003/linder-2003.pdf
December 2012.

[5]

M. Melis, Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt
Splashdown
Using
an
Arbitrary
Lagrangian-Eulerian
Approach.
NASA/TM--2003-212093.
2003.
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20030016601_2003020325.pdf
Accessed December 2012.

[6]

L. Souli, M. and Olovsson, “ALE and Fluid-Structure Interaction Capabilities in
LS-DYNA”, in: Proceedings of the 6th International LS-DYNA Users Conference, Detroit,
USA,
2000,
http://www.dynalook.com/international-conf-2000/session15-4.pdf
Accessed December 2012.

[7]

C. Stoker, “Developments of the Arbitrary Lagrangian-Eulerian Method in non-linear Solid
Mechanics.”, PhD thesis, Universiteit Twente, The Netherlands (1999): 152.
http://doc.utwente.nl/32064/1/t0000013.pdf Accessed December 2012.

[8]

T. M.-S. Corporation, Bird Strike Simulation Using Lagrangian & ALE Techniques with
MSC/DYTRAN.

[9]

J. P. Barber, H. R. Taylor, J. S. Wilbeck, “Characterization of Bird Impacts on a Rigid
Plate: Part 1”, Technical report AFFDL-TR-75-5, Air Force Flight Dynamics Laboratory,
Wright-Patterson Air Force Base, OH (1975).

[10]

W. Moffat, Timothy J. and Cleghorn, “Prediction of Bird Impact Pressures and Damage
using MSC/DYTRAN”, in: Proceedings of ASME TURBOEXPO, Louisiana, 2001.

[11]

R. S. Bertke, J. P. Barber, “Impact Damage on Titanium Leading Edges from Small Soft
Body Objects”, Technical Report AFML-TR-79-4019, Air Force Flight Dynamics

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131

Laboratory, Wright-Patterson Air Force Base, OH (1979).
[12]

V. K. Goyal, C. A. Huertas, T. J. Vasko, Bird-Strike Modeling Based on the Lagrangian
Formulation Using LS-DYNA. American Transactions on Engineering & Applied
Sciences, 2(2): 57-81. (2013) http://TuEngr.com/ATEAS/V02/057-081.pdf Accessed
March 2013.

[13]

V. K. Goyal, C. A. Huertas, T. R. Leutwiler, J. R. Borrero, T. J. Vasko, Smooth Particle
Hydrodynamics for Bird-Strike Analysis Using LS-DYNA. American Transactions on
Engineering
&
Applied
Sciences,
2(2):
57-81.
(2013)
http://TuEngr.com/ATEAS/V02/083-107.pdf Accessed March 2013.

[14]

B. N. Cassenti, Hugoniot Pressure Loading in Soft Body Impacts. United Technologies
Research Center, East Hartford, Connecticut, 1979.

[15]

T Belytschko, WK Liu, B Moran, Nonlinear Finite Elements for Continua and Structures,
John Wiley & Sons, New York, 2000.

Dr. V. Goyal is an associate professor committed to develop a strong sponsored research program for
aerospace, automotive, biomechanical and naval structures by advancing modern computational
methods and creating new ones, establishing state-of-the-art testing laboratories, and teaching
courses for undergraduate and graduate programs. Dr. Goyal, US citizen and fully bilingual in both
English and Spanish, has over 17 years of experience in advanced computational methods applied to
structures. He has over 15 technical publications with another three in the pipeline, author of two
books (Aircraft Structures for Engineers and Finite Element Analysis) and has been recipient of
several research grants from Lockheed Martin Co., ONR, and Pratt & Whitney.
C. Huertas completed his master’s degree at University of Puerto Rico at Mayagüez in 2006.
Currently, his is back to his home town in Peru working as an engineer.

Dr. Thomas J. Vasko, Assistant Professor, joined the Department of Engineering at Central
Connecticut State University in the fall 2008 semester after 31 years with United Technologies
Corporation (UTC), where he was a Pratt & Whitney Fellow in Computational Structural
Mechanics. While at UTC, Vasko held adjunct instructor faculty positions at the University of
Hartford and RPI Groton. He holds a Ph.D. in M.E. from the University of Connecticut, an M.S.M.E.
from RPI, and a B.S.M.E. from Lehigh University. He is a licensed Professional Engineer in
Connecticut and he is on the Board of Directors of the Connecticut Society of Professional Engineers

Peer Review: This article has been internationally peer-reviewed and accepted for
publication according to the guidelines given at the journal’s website.

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