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Figure 11-13. Aggregate foam material environmental test specimens pre-test (left) and post-test (right).
specimens were oven dried to eliminate the absorbed water water immersion, therefore, is the cause for the observed
mass (Figure 11-13). degradation.
Following the environmental tests, the specimens were sub- Overall, these tests indicate that the aggregate foam mat-
jected to a confined cylinder compression test (Figure 11-14) erial should be protected from immersion conditions caused
to determine the performance degradation. When compared by standing water. Additional testing could be conducted to
with the fresh material, the samples exhibited a 47% decrease characterize durability in non-immersion scenarios where
in energy absorption capacity. a drainage bed approach is used. For the waterproof bed
Mechanically, the closed-cell microstructure of the foam approach using a fully sealed plastic envelope, degradation
limits water absorption such that water penetrates only the over time is not anticipated.
outer-most open pores of the foam. Upon freezing, the expand-
ing water cracks the cells, permitting progressively deeper pen- 11.4. Modeling Effort
etration into the specimen as the cyclical testing proceeds. The
degradation observed is, therefore, not surprising. The modeling effort involved several stages, as shown previ-
These environmental tests represent the most severe of ously in the flowchart of Figure 11-5. A high-fidelity model for
circumstances, where the specimens were fully immersed in the aggregate foam material was calibrated to match the test
data (Figure 11-5, block 1). Using this material model, an
water, without normal countermeasures of drainage or a pro-
arrestor bed model was constructed and coupled with tire
tective plastic envelope. Information provided by the manu-
models for the different aircraft (Figure 11-5, block 4). Finally,
facturer indicates that cyclical temperature and humidity
large batches of simulations were conducted using these paired
alone do not degrade the material over time. The presence of
models, which generated volumes of data for use by the APC
(also block 4).
This section will discuss the arrestor model development
and batch simulation process. Performance predictions for
the aggregate foam arrestor concept are reserved for the fol-
lowing section (Section 11.5).
11.4.1. Selection of Modeling Approach
Of the three candidate systems evaluated, the aggregate
foam concept was the most difficult to represent with a robust
high-fidelity computer model. Because it had both loose
aggregate and crushable foam properties, it did not readily fit
into existing material models.
Two modeling code choices were available:
Figure 11-14. Confined cylinder testing of aggregate 1. LS-DYNA is a general purpose FEM code that supports
foam environmental test specimen (post-test). multiple numerical methods. LS-DYNA could readily sup-
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port crushable material models. However, loose aggregates solids in a way that allows large dislocations, permitting the
could only be represented by defining many separate pieces material to move over and past itself. The SPH methodology
of material and allowing them to interact on the basis of enhanced the continuum representation of the material.
defined contacts between the pieces. This approach repre- Additionally, because the material acted as a continuum, this
sented a computationally expensive path that would have was assumed to at least partially represent the turf layer's
required infeasible simulation times. mild confinement effects on the bed.
2. EDEM is a DEM code that supports the modeling of hard
aggregates. EDEM could readily model massive beds of
11.4.2. Smoothed Particle Hydrodynamics
aggregate pieces while maintaining efficient simulation
Formulation
times. However, EDEM did not support crushable material
modeling of any kind. The aggregate foam arrestor models were developed in LS-
DYNA, a general-purpose finite element modeling code.
In light of these considerations, some simplifying assump- Within LS-DYNA, a number of formulations exist for repre-
tions were made, and LS-DYNA was selected to model the senting solids and fluids. Due to the high compressibility of
material using a crushable foam model. The model represented the aggregate foam material and its loose fill properties, an
the aggregate foam as a continuum of material (Lagrangian), SPH mesh-free formulation was employed. SPH offered the
rather than representing individual pieces of crushable foam. ability to represent high-dislocation solids with accuracy
Because the material definition did not discretely represent the while maintaining time-efficient simulations.
separate pieces of the material, the aggregate mode of behavior Because SPH uses particles instead of the more typical
was not captured by the model. This was deemed an acceptable finite elements, the illustrations in this section depict the
loss in fidelity based on several assumptions: material as a collection of small spheres. Although it would be
desirable given the nature of the aggregate foam material,
1. Dominant Mode of Energy Absorption. As the hydrostatic these particles do not represent disjointed pieces of aggregate.
compression tests showed, the majority of the energy Rather, they are mathematically interconnected to represent
absorption for the material takes place in the solid regime of a continuous solid material (Lagrangian formulation).
behavior, rather than the aggregate regime (Section 11.3.3).
About 95% of the energy absorption capacity of the material
exists when the material behaves in a solid-like fashion. 11.4.3. Calibration to Physical Tests
2. Cover Layer Effect. In arrestor applications, the aggregate- 11.4.3.1. Constitutive Model
type behavior would appear in the uppermost portion of
the arrestor bed, where the confinement pressures are low LS-DYNA currently offers about 200 constitutive models; of
and the pieces are allowed to flow past and roll over one these, about 18 are applicable to various foams. Based on prior
another. This upper portion of the aggregate would likely experience and on a review of the LS-DYNA keyword manual,
spray forward and away from the tire, as with solid aggre- several candidates were singled out for evaluation. After some
gate arrestor beds. Material projected away from the tire experimentation, *MAT_CRUSHABLE_FOAM was selected
would not participate significantly in the arresting process, as the best overall choice. This material model has parameters
decreasing the effective thickness of the arrestor bed. as given by Table 11-2. The calibration process required defin-
However, the design concept includes a cover layer that ing these material parameters such that the model performance
would attenuate or prevent this spray from occurring. The matched that of the physical material tests.
aggregate at the top would presumably be held in place
until overrun by the tire and preserve the effective bed Table 11-2. Parameters for *MAT_063 or
thickness. *MAT_CRUSHABLE_FOAM.
3. Material Density. Unlike a hard aggregate arrestor bed,
the foam aggregate has a low density (11 pcf). This leads Parameter Symbol Description
to minimal mass-based momentum transfer effects, which MID Material ID number
can occur when an aggregate is projected, or sprayed, at RO Density
high speed. Because the material is light, the momentum E E Young's modulus
effects would be much less significant than the energy PR Poisson's ratio
absorbed by material compaction.
LCID Load curve ID for nominal stress versus strain
4. SPH Formulation. Within LS-DYNA, the material was rep-
TSC Tensile stress cutoff
resented using an SPH formulation. While this formula-
DAMP Rate sensitivity via damping coefficient
tion does not represent aggregate particles, it does represent
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The constitutive model assumes a normal homogeneous Attempts were made to calibrate the model to also match the
crushable foam material. In a typical foam, the compressibil- hydrostatic triaxial specimens. These specimens were somewhat
ity derives from the presence of voids within the cells of the difficult to model due to a nuance of the SPH formulation,
foam microstructure. However, the aggregate foam includes which proved challenging to fit with a hydrostatic membrane
not only these microstructure void spaces (in each aggregate load. Application of high confinement pressures led to instabil-
piece) but also larger voids between the aggregate pieces. ities due to the low initial slope of the material compression
The approach taken for applying this material model was curve. Since the aggregate foam material exhibited minimal
to match the overall net behavior of the material. The load pressure dependence for the higher confinement pressures (Fig-
curve definition (LCID) was therefore defined per the con- ure 11-10), this was deemed a low-priority calibration point.
fined cylinder test data, with an exponential shape. In testing,
this shape was produced by the sum of the microstructure 11.4.4. Tire and Arrestor Simulations
compression and inter-particle void space compaction.
Using this material model, the same summed behavior was Using the calibrated aggregate foam material model previ-
assumed. ously described (Section 11.4.3), a large-scale arrestor model
was created in LS-DYNA to simulate overruns by aircraft
tires. Figure 11-16 illustrates the model with a 36-in. depth
11.4.3.2. Material Calibration Model
and a B737-800 main-gear tire (Goodyear H44.5x16.5) at
A confined cylinder calibration model (Figure 11-15) was 50% penetration depth.
developed to determine the best-fit properties for the consti- No turf cover layer for the bed was included in the model.
tutive model. The material parameters of the model were Several possible turf layer designs were feasible, each with
optimized using LS-OPT, an optimization software package different thicknesses and material properties. It was assumed
developed by LSTC, the makers of LS-DYNA. LS-OPT ran the that, while a turf layer would confine the top layer of aggre-
simulations in batches iteratively. After each iteration, it nar- gate foam to prevent spraying, it would optimally not affect
rowed the region of interest, effectively zooming in closer to the mechanical response substantially. Because the spraying
the predicted optimum calibration point. After 5 iterations of behavior was inherently mitigated by the continuum repre-
18 simulations each, the design was optimized for a best-fit set sentation of the material, a discrete top layer was not neces-
of material parameters. sary to determine the characteristic arrestor response.
Table 11-3 gives a summary of the calibration process, As Figure 11-17 shows, the compressed material area extended
including the final accuracy of the calibrated model. all the way to the bottom of the arrestor bed, which was in con-
Figure 11-15. confined cylinder model for aggregate foam
material calibration.
Table 11-3. Specifications for aggregate foam material calibration.
Test to Replicate Description Error of
Calibration
Confined Cylinder ˇ 12.375 x 9.5-in cylinder
Compression Test
ˇ Match stressstrain load curve with RMSE to 75% <2.0%
compression
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Small Pieces of Aggregate
Foam Fragment Off of Bed Deformable Finite
Element Aircraft
Tire Model
SPH Arrestor Bed
Arrestor and Tire
Model Uses Half-
Symmetry
Tire Penetrates
Vertically to a
Prescribed Depth
Material
Compressed
by Tire
Figure 11-16. Model of combined tire and aggregate foam arrestor system.
trast to the localized compression region for the solid foam zone. These behaviors are consistent with the anticipated
block candidate (Section 9.4.3). Waviness in the rut sidewalls mechanical response of the aggregate foam material.
and a longer compression region in front of the tire were also
manifest. Figure 11-17 shows that under a static downward
11.4.4.1. Arrestor Bed Models
load, the material exhibited a pyramid-shaped compression
The arrestor bed models were constructed using half-
symmetry to reduce computation time. They varied in size
depending on the aircraft tire being used. The bed length was
determined by the distance required for the tire to make a
certain number of rotations, such that the loading settled to
a steady-state condition. The bed width was determined by
the tire width, such that artificial boundary effects were min-
imal and the response approximated that of a wide bed of the
material. The smallest bed, used for the 18-in. nose tire of the
CRJ-200, was 120 in. long and 9 in. wide. The largest bed,
used for the 49-in. main tire of the B747-400, was 300 in. long
and 36 in. wide.
All beds were constructed with a 36-in. depth. However,
the effective depth of the bed was adjusted by use of a mov-
able rigid plane (Figure 11-18). Only the upper part of the
Pyramid-Shaped Compression Zone material, above the rigid plane, was involved in the overrun
Figure 11-17. Compression zone under tire without compression. This approach enabled various depths to be
forward motion. rapidly configured within a single arrestor bed model.
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Rigid Plane at 18-
inch Depth
Only Upper Part of Material
36-inch Involved in Compression
Deep Bed
Figure 11-18. Adjustable height of aggregate foam arrestor bed.
SPH particle sizes were chosen based on the tire size. An error required to create stable, fast-running simulations. These two
estimation process was undertaken to determine the required factors were additional complications that were not present in
particle size to maintain an acceptably low discretization error. the EDEM aggregate simulations. However, the inclusion of
For the larger tires, a 2-in. particle size was found to have less these factors led to higher-fidelity results.
than a 4% error for the predicted drag and vertical loads. For From a mechanical standpoint, as the axle of the wheel
smaller tires, the particle size was reduced to 1 in. to maintain penetrated the bed vertically, both the tire and the arrestor
similar size proportionality. Based on the particle and bed size material underwent compression. The interplay of the tire
variations, a typical bed model had nominally 45K particles. and arrestor compression created oscillations in the mea-
sured loads. This oscillating behavior was further amplified
by the free-spinning nature of the tire. Eventually the tire
11.4.4.2. Tire Models would settle to a constant rate of rotation, which proved to
The tire models were fully deformable FEM, as discussed be a function of the forward speed, depth, and interface
in Appendix F. Table 11-4 summarizes the tire models devel- friction. It was found that a minimum forward travel dis-
oped. Each tire model was calibrated to match the actual tire's tance was required for the loads and rotation to reach
load-deflection performance up to 80% of the maximum steady-state conditions before load measurements could
bottoming load. This 80% load became a limit criterion dur- be made.
ing the batch simulations. Sequencing options included several factors:
The deformable nature of the tires produced an accurate
representation of the interface between the tire and the arrestor ˇ Prescribed vertical penetrations versus prescribed vertical
material. As the load on the tire increased due to deeper bed loads;
penetration, the contact area became flatter with an increased ˇ Applying the vertical penetration/load before or after
surface area. This shape change created a corresponding beginning the forward motion; and
increase in the load on the tire. ˇ Applying the forward motion before or after making con-
tact with the bed
11.4.4.3. Sequencing of Simulations Depending on the sequencing method used to accelerate
Because the tires in the LS-DYNA simulations were deform- the tire and set the penetration depth, the initial oscillations
able and were allowed to spin freely, a sequencing method was could be more or less severe. This in turn could require longer
or shorter simulation times, and longer or shorter arrestor
Table 11-4. FEM tire library for beds. Because the arrestortire models were to be run repeat-
aggregate foam arrestor models. edly in large batches, it was important to develop a sequenc-
ing methodology that would produce efficient simulation
Aircraft Landing Gear Tire Designation run times.
CRJ-200 Main Gear H29x9.0-15 Multiple methods were attempted through experimentation
Nose Gear R18x4.4 before settling on the approach illustrated by Figure 11-19. The
B737-800 Main Gear H44.5x16.5-21
tire was first pressed downward into the material to a pre-
scribed depth. Then the tire was accelerated to the desired for-
Nose Gear H27x7.7-15
ward speed and spun-up to an initial rotation speed (typically
B747-400 Main Gear H49x19-22
about one-third of the ideal rotation rate expected on hard
Nose Gear H49x19-22
pavement). The prescribed spin rate was then released, allow-
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Tire begins above arrestor
Tire presses down into arrestor
Tire accelerates forward and
is given an initial spin rate
Tire continues forward
and is allowed to freely
spin
Steady-state vertical
and drag loads are
measured
Figure 11-19. Sequencing method for aggregate foam arrestor model.
ing the tire to settle to a natural rotation rate, while the forward 11.4.5.1. Methodology
motion continued at a constant speed. After the oscillations
Batch simulations were conducted for each tire with three
settled out of the system, the steady-state vertical and drag
open variables:
loads were measured.
The final result was an accurate prediction of the loads on ˇ Speed, from 10 to 70 knots (Speeds below 10 knots were
the tire under free-spinning un-braked conditions. impractical due to the long simulation times required for
a tire to travel the required minimum distance. Loading at
speeds below 10 knots was based on the extrapolated meta-
11.4.5. Batch Simulations
model data fit.);
Using the arrestor bed model, large batches of simulations ˇ Bed depth, in incremental depths from 3 to 36 in. (Fig-
were conducted to generate substantial bodies of data for a ure 11-20); and
wide range of overrun conditions. This data was then assem- ˇ Penetration into the bed, from 10% to 100% of maximum
bled into "metamodels" for uploading and use by the APC. penetration depth.
Penetration Tire Rut Depth
Depth Deflection
Bottoming
Depth
Bed Depth
Figure 11-20. Depth definitions for aggregate foam bed models.
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Due to the two sources of compression (arrestor material metamodels were RBF networks, which can effectively capture
and tire), the definition for penetration depth was more com- non-linear behaviors including multiple concavity changes
plex than for the rigid tire approach used for the aggregate across the data set.
arrestor models. Two conditions defined the maximum pen- Table 11-5 summarizes the fit quality for the metamodels.
etration depth: The RMS error showed the highest variation among the three
candidates simulated, which was typically below 7%, but had
1. The maximum penetration depth was considered to be three instances of higher values for the 29-in. and 18-in. tires.
85% of the bed depth (fully compressed material) plus the The R-squared value was typically above 0.97, but again
deflection of the tire at 80% of the bottoming load. Beyond dropped below 0.95 for the 18-in. tire. Typically, these prob-
this degree of penetration, the tire models were no longer lems would be resolved by adding additional simulation points.
accurate. In this case, however, the scatter in the data persisted even
2. For small tires in deep beds, the maximum penetration when more simulations were conducted.
was further limited to be no greater than the tire diameter. A closer examination of the batch simulation output reveals
At depths beyond this, the simulations often did not settle that the cases most responsible for the scatter involve deeper
to steady-state conditions. arrestor beds. Because the material essentially has a depth-
varying quality to it, with an exponentially shaped load curve,
The large batch simulations were conducted using LS- it tended to exhibit slipstick behavior under the tire. The
OPT. Based on the initial model files, LS-OPT generated material would compact into a clump until enough force
permutations with various speeds, bed depths, and penetra- was built up for a section to break free, forming a fissure. Two
tion levels. It sequentially executed the simulations and potential solutions to this data scatter would have involved
extracted the load data from them. Generally, the batches (1) longer rolling distances in the simulations with corre-
were conducted in multiple iterations of 10 simulations spondingly increased run times, and (2) revisions to the con-
each. Additional iterations were added to improve accuracy stitutive model for the aggregate foam material. Project time
as needed. and budget constraints prohibited further pursuit of improve-
ments, so the existing metamodels were used.
As the table shows, the points used in the metamodels were
11.4.5.2. Summary Tables of Metamodels
often less than the total number of simulations conducted.
The output from the batch simulations was extracted and This discrepancy was caused by simulations that failed prior
assembled automatically by LS-OPT, where metamodels to termination due to tire overloading, or simulations that
were constructed for the drag and vertical load forces. Meta- had not adequately settled to steady-state conditions for
modeling is analogous to fitting a curve through experi- accurate load measurement. The smaller tires experienced a
mental data, except it is applied to multi-dimensional data greater percentage of omitted runs than the larger tires due to
sets. These data sets were four-dimensional, including speed, the relative loading severity and greater proportional pene-
depth, penetration, and load (either vertical or drag). The tration depths.
Table 11-5. Metamodel accuracy summary for aggregate foam
arrestor bed.
Simulations Points
Tire Response RMS Error R2
Conducted Used
Drag 7.10% 0.995
H49 50 50
Vertical 5.96% 0.994
Drag 3.57% 0.999
H44 60 58
Vertical 3.05% 0.998
Drag 16.70% 0.971
H29 60 47
Vertical 7.70% 0.986
Drag 3.39% 0.998
R27 40 40
Vertical 3.78% 0.997
Drag 23.80% 0.948
H18 80 73
Vertical 21.40% 0.943
