S. RamaprasadCenter of Excellence, Aerospace and Defence,

Satyam Computer Services Private Limited,

Bangalore 560100

Simulation of Bird Strike on Aero Structures Using Explicit Finite element Methods

A Bird Strike is a collision between a bird and a aircraft. It is serious

threat to aircraft flight safety and has caused a number of accidents with

human causalities. According to Federal Aviation Regulation wildlife

strikes like the bird hit has caused the civil aviation industry considerable

costs and resulted in significant reduction of flight downtime hours. An

aircraft must show compliance with “continued safe flight and landing”

requirements following specified types of high-energy bird impact. Hence

it is now imperative to design aircraft components capable of withstanding

these impacts

To obtain certification from the FAA, an aircraft must be able to land after

an impact with a 4 pound bird at any point in the aircraft. For new jet

engines designs, the FAA certification requires more tests for medium and

large bird ingestion. For the medium or flocking bird requirement, an

engine must be capable of operating for five minutes with less than 25%

thrust loss after impacting several 1.5 pound or 2.5 pound birds. For the

large bird ingestion test, the engine must be able to withstand a 6 pound or

8 pound bird and achieve safe shutdown. As a consequence the aviation

authorities require that none of the vital, forward facing elements of

aircraft structures should fail as a result of bird strike. These requirements

have serious effect on the production cost, as each new design must

incorporate the value of the full-scale testing. However, significant

savings can be achieved in the design and manufacture of elements of

aircraft structures by employing the state-of-the-art predictive modeling

techniques thus ensuring that the very first full-scale bird strike

certification tests are successful. Presently, major improvements are

expected in minimizing the consequences of bird ingestion into aircraft

engines and bird strike against leading edges of wing structures. Recent

advances in measurement instrumentation and computing have allowed

for the investigation of a wider spectrum of physical phenomena

surrounding bird strike impact on aircraft structures. Accordingly, the

ability to predict accurately the observed mechanisms of soft body impact

and to provide information on the magnitude and distribution of surface

pressures during such events becomes vital and hence pre-requisites to

reliable design of aircraft structures. Numerical simulation tools based on

the finite element method have reached such level of maturity that these

can be used confidently for dimensioning of structural elements subjected

to normal service loads. However, the ability to assess the behavior of

bird-like soft-bodied projectiles and to predict the integrity of structures

subjected to such loading to simulate the observed large deformations and

erosion of soft-bodied projectiles needs to be carried out with adequate

accuracy.

This article describes different simulation strategies to arrive at a robust

methodology for an accurate assessment of the bird impact event. This

model must be able to reproduce both impact and loads generated in a

bird-strike event. A good approximation for the model is the finite

element method because of its ability to analyze complex geometries,

material and load non-linearity, and study the interaction between the

bird and the target. Various finite element methods are used to model the

impact phenomena. Typically explicit finite element codes like LS-Dyna

are used to study the bird impact event. Explicit formulation of the finite

element method allows us to accommodate nonlinear effects involving

both geometric and material nonlinearity. LS Dyna is a general purpose

explicit finite element program used to analyze the nonlinear dynamic

response of three-dimensional structures. It includes an automated contact

analysis capability and error-checking features which gives the

opportunity to solve complex crash and impact problems. LS-DYNA

simulation results have been consistently correlated with experimental

data which give high confidence in using the program as an accurate

simulation tool.

The transient dynamic equation of motion for describing the motion of the

shell is given by

,

(1)

In the above equations, the Finternal is contributed by stiffness terms while

Fcontact is derived by a suitably chosen contact interaction algorithm. There

are many different contact algorithm which could be chosen, however the

frequently used contact algorithm is a surface to surface contact

interaction . The contact algorithm allows us to calculate the force

generated at the interface between the target and the Bird. Belytschko

Tsay formulation is predominantly used for shell modeling for

determining the dynamic response and Hourglass control is invoked to

achieve better accuracy of the results.

Due to the conditional stability of the explicit time integration scheme, the

time step calculation plays a very important role for its performance.

Larger time steps decrease the computational effort for solving the

problem, but if a limit called critical time step, tcr, is exceeded the

solution rapidly diverges. To be able to efficiently use, the well known

expression for the critical time step

, (2)

a simple estimate of the highest natural frequency max is required. In LS

DYNA the simple effective calculation of time step is carried out using

the characteristic length of the element and the sound speed

There are typically three different methods used for simulation of the bird

impact event. These are the Lagrangian method, Arbitrary Lagrangian

Eulerian formulation, and the Smooth Particle Hydrodynamics.

Lagrangian Approach: When the Lagrangian solver is used, grid points

are fixed to locations on the body being analyzed. Elements of material

are created by connecting the grid points together, and the collection of

elements produces a mesh. As the body deforms, the grid points move

with the material and the elements distort. The Lagrangian solver is,

therefore, calculating the motion of elements of constant mass This is

contrary to Eulerian approach where the grid points are fixed in space and

the elements are simply partitions of the space defined by connected grid

points. Numerical problems due to element distortions limit the

applicability of Lagrangian description of motion when modeling large

deformation process. On the other hand the Eulerian decription in which

the material flows through a mesh fixed in space can completely avoid

mesh distortion problems. The Eulerian approach though is not devoid of

instabilities and its applicability is limited by the dissipation and

dispersion problems associated with the fluxing of mass across element

boundaries. The Bird is usually modeled as Hexahedron elements while

the target could be modeled either as brick or shell elements. Graded mesh

shall be used with finer mesh used near the impact zone. To simulate the

residual stresses in the radial direction, cross-section near the impact zone

will have sufficient element density. Sufficient iterations in terms of mesh

density needs to be carried out to achieve convergence of computed

residual stresses. For the purpose of simulation, two parts shall be created

one for the Bird and another for the target. Cowper Symonds strain rate

parameters or different stress strain curves for different strain rates must

be supplied to capture the strain rate effects accurately. Necessary

boundary conditions shall be specified using the *BOUNDARY_SPC

control card. Impacting body’s velocity can input directly using the

*INITIAL_VELOCITY control card. The height between the Bird and the

target shall be maintained very small for solid elements. For shell element

modeling the height shall be maintained at marginally higher than the

average thickness of the Bird and the target thickness.

The contact interaction between the Bird and the Target can be defined

using the *CONTACT_NODES_TO_SURFACE for solid to solid

interaction and *CONTACT_SURFACE_TO_SURFACE for solid to

shell interaction. The time for analysis should be carried out for sufficient

length of time to get the correlation accurately for the deformation under

impact. Hour glass control shall be exercised to remove all zero energy

modes and to ensure the model reproduces the correct rigid body motions.

Augmented Lagrangian Eulerian Approach is known as the ALE

Formulation: An Alternative to Lagrangian approach is a method known

as ALE Formulation. In this formulation a portion of the structure (usually

a projectile or impactor) is modeled with an Eulerian mesh which can only

accept volume mesh and the active space also called void needs to be

meshed (with volume mesh )as well with different materials properties

from the impactor. The projectile or the impactor are decribed by Eulerian

mesh because the Lagrangian decription is not suited to model them as

they undergo large deformations. The computational cost of this method is

quite high since these meshes have to span the entire active space

covering all Lagrangian structures which is usually the targets. This

method shall require an Eulerian Lagrangian Coupling algorithm to

combine its motion with Lagrangian parts of the model. Here the target

shall be modeled with either Lagrangian solid or shell meshes. Finer mesh

shall be used near the zone of impact. The Bird and the space between the

Bird and the Target shall be modeled with an Eulerian solid mesh. The Air

space shall cover the entire Target as well as the Bird. For assigning

section properties to Eulerian mesh the *SECTION_PROPERTY_ALE

card should be used. Different contact method (Penalty and Constraint)

can be employed to assess the convergence of results. A standard ALE

formulation shall be employed for the simulation. Hour glass control shall

be exercised to remove all zero energy modes and to ensure the model

reproduces the correct rigid body motions. Appropriate material model

should be employed to model the Target for the simulation. The coupling

between the Lagrangian and Eulerian Mesh shall be established using the

*CONSTRAINED_LAGRANGE_IN_SOLID control card. The surface

of the Eulerian Mesh representating the Bird should be assigned as the

master set and the plate surface of the target shall be represented as the

slave set. The Contact interaction between the plate (modeled as solid

element) and the gelatin (Eulerian mesh) shall be defined using the control

card *CONTACT_NODES_TO_SURFACE control card, while for the

Target (modeled as a shell element) and the Bird, the contact interaction

shall be defined using the *CONTACT_SURFACE_TO_SURFACE

control card. Analysis can be carried out assuming zero friction during the

contact interaction. The density for both the Bird and the void mesh shall

be specified using the Material control card *MAT_NULL. The density

for the Void mesh shall be prescribed as the Air density If the Target is

modeled with a shell formulation, the *SECTION_SOLID control card

shall be used to specify the shell thickness for the Target elements.

Meshless methods like Smooth Particle Hydrodynamics (SPH): SPH

is a meshless lagrangian numerical technique used to model the fluid

equations of motion. SPH has proved to be useful in certain class of

problems where large mesh distortions occur such as high velocity

impact, crash simulations or compressible fluid dynamics. With the

SPH technique, both the structure and fluid can be modeled using a

Lagrangian approach. The SPH technique utilizes a meshless

Lagrangian method to represent fluids. In the SPH method, the fluid

material is treated as particles that have their masses smoothed in

space. Coupling between the SPH grid points and the structural

model is accomplished through normal contact definitions. The

projectile/ or Bird in this case shall be numerically represented by

few thousand (4000-5000) SPH particles. While the target shall be

modeled using solid or shell elements. The SPH particles shall be

assigned material properties, hence will have dual function i.e

approximation points and material components. These particles are

capable of moving in space, carry all computed information, and thus

form the computational frame for solving the partial differential

equations describing the conservation laws. The particles indicate the

gradation of the SPH particles. Because the SPH model is

represented by a group of elements or small spheres, and is not

continuous along the whole space they are occupying, it is necessary

to calculate the physical properties for each element by taking into

account that each element should have the same bird density. It is

also important to highlight that the sum of masses of all small

elements or spheres must be equal to the mass of the bird. The

following equation shows how the lumped mass for each SPH

element is calculated:

Lumped mass =

Note that the number of nodes is equal to the number SPH elements.

The *MAT_NULL shall be assigned to the SPH particles since they

are used to represent the gelatin. The constant for smoothing shall be

taken as 1.2 unless advised otherwise. The contact interaction type

shall be varied between Surface to Surface and Node to surface to

both the simulation involving target meshed with solids and shells.

In the all the fore-mentioned studies, Bird should be modeled using

elastic-plastic-hydrodynamic material model with polynomial

equation of state. For the Eulerian Mesh representing the Bird, the

equations of state coefficients (C1, C2,..CN) are supplied using the

*EOS_TABULATED control card for the Bird part.

Material Models: In all types of impact analysis it is not possible to

correlate the analytical results with experiments unless we use an

appropriate material model. The material model should be able to capture

the stain rate effects appropriate. For all the tree types of simulation

problem an appropriate material model depending on the target material

shall be employed. Usually for isotropic material for simulation of soft

body impact on a hard target the Material model 24 is predominantly

used. This material model can be chosen using the

*MAT_PIECEWISE_LINEAR_PLASTICITY control card in LS DYNA.

This is piecewise linear plasticity material model which can accommodate

strain rate effects by any of the following three options, Strain rate may be

accounted for by using the Cowper Symondsmodel which scales the yield

stress with the factor

Where C and p are called the Cowper Symonds strain

rate parameters to be defined by the user. These

values could be supplied on the material card

parameter list.

1. .For complete generality a complete load curve

defining b which scales the yield stress may be

supplied.

2. The most popular method is to supply different stress

strain curves for different strain rates.

The appropriate material model for the bird material is *MAT_NULL

material model.

Hour Glass Control: Hourglass energy is often a problem with the

reduced element formulations used in explicit analysis codes. Controlling

the hourglass energy is done by using *CONTROL_HOURGLASS or

*HOURGLASS. Option 2 (default viscous hourglass control) is typically

used for this type of analysis. Viscous control is recommended for high

velocity deformations.

Conclusions

Robust methodology for Bird impact simulation must be established in

order to achieve acceptable test correlation without which it is not

possible to get FAA Certification to ensure that Aircraft Flight safety is

not impaired under a Bird strike event. .Three Simulation techniques using

a Explicit finite element code LS DYNA for the predictive modeling of

bird impact on Aerospace structures has been discussed in this article. The

relative advantages and disadvantages of each method have been

elaborated. Details on the modeling aspects using each method are

explained.