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CHAPTER 12
Depth-Varying Foam Material
As a companion effort to the ACRP research, additional 12.2. Depth-Varying
graduate-level research was undertaken to explore a depth- Profiles Considered
varying foam material concept. A summary of that research
is given in this chapter. For an in-depth examination, the Multiple depth profiles for the material were possible. Fig-
original research document should be consulted (33). ure 12-2 illustrates three simple profile types that were con-
The goal of the study was different from that of the full sidered, as well as a depth-invariant material, which represents
the current homogeneous arrestors. The curves have been
system concept evaluations in Chapters 9 through 11. The
normalized to compare overall trends.
evaluation of the depth-varying concept did not include
Viewing the profiles shows that the linear and quadratic
full aircraft arrestment simulations. Instead, it was con-
cases sit astride the exponential function, given the same start-
fined to a narrower study of the effects of the material on
ing and ending points. As such, the exponential case did not
two different tires: the main-gear tires of the CRJ-200 and
seem to offer novel content, and the evaluation was narrowed
the B737-800. While the likely arresting performance can
to include three profiles:
be inferred based on the results, APC simulations were not
conducted. 1. Constant (baseline),
2. Linear profile, and
12.1. Depth-Varying Foam Concept 3. Quadratic profile.
By its nature, an arrestor bed installed at an airport is a sin- 12.3. Modeling Approach
gle, static system. It must arrest any and all aircraft that could
overrun the runway end, from large B747s down to small The modeling approach for the depth-varying material eval-
regional jets. Problematically, these aircraft differ in ways that uation was essentially the same as for the glass foam material
have a significant effect on arresting efficiency; the arrestor (Section 9.4). Only points of contrast in the methods will be
slows some aircraft more quickly than others. discussed in this section.
To improve the one-size-fits-all performance of an arrestor
bed, a depth-varying foam arrestor material was investigated. 12.3.1. Calibration of Material Model
The cellular cement used in existing EMAS arrestors is homo-
Material calibration was not undertaken because the eval-
geneous, having the same density and strength throughout uation involved idealized materials. All three material options
each block of material. Changing the density and strength to assumed zero Poisson ratios, which is consistent with typical
become harder at deeper levels could potentially achieve a crushable foam behaviors. Figure 12-3 illustrates the idealized
degree of performance leveling between large and small air- compression load curve for the material model.
craft (Figure 12-1).
This concept was evaluated using an idealized foam
12.3.2. Tire and Arrestor Simulations
material model rather than a particular type of crushable
foam (cement, polymer, glass, etc.). Many crushable foam As with the glass foam material evaluation, the arrestor
options exist, and depth-varying layups for many could be models were constructed in LS-DYNA using the deformable
achieved. FEM tire models and SPH arrestor beds (Figure 12-4).
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Compression
Stress ()
Material
Becomes
Harder Plateau Slope
Figure 12-1. Depth-varying material concept.
Energy Absorbed in
Compression
Compression
A large-scale arrestor model was created in LS-DYNA to Strain ()
simulate overruns by aircraft tires. No protective cover layer
for the bed was included in the model, and it assumed a con-
Figure 12-3. Idealized crushable foam
tinuous material without seams. stressstrain compression curve.
12.3.2.1. Arrestor Bed Models Each part/layer had its own material definition based on its
The arrestor bed models were constructed using half- depth. Experiments showed that each layer required at least
symmetry to reduce computation time. They varied in size two rows of SPH particles in order to initialize properly. The
depending on the aircraft tire being used. The bed length was 30-in. deep arrestor, with 2-in. particles, had eight separate
determined by the distance required for the tire to make a layers (Figure 12-5).
certain number of rotations such that the loading settled to a
steady-state condition. The bed width was determined by the 12.3.2.2. Tire Models
tire width such that artificial boundary effects were minimal
and the response approximated that of a wide bed of the The tire models were fully deformable FEM, as discussed
material. The beds were 36 in. wide, 300 in. long, and 30 in. in Appendix F. However, for this limited study, only the
deep. However, the effective depth of the bed was adjusted by main-gear tires for the B737 and CRJ-200 were used. The goal
use of a movable rigid plane. was to observe the behavioral trends, from which likely
For the 44.5-in. tire, the SPH particles were sized at 2 in., arresting performance was inferred. Table 12-1 summarizes
but the smaller 29-in. tire used a bed with 1.5-in. particles to the tires that were used in the evaluation.
maintain a low discretization error.
The depth-varying arrestor bed featured a division of the 12.3.2.3. Sequencing of Simulations
SPH material into several parts, forming stratified layers.
The sequencing method for this evaluation differed from
that of the foam glass evaluation. Because a full metamodel of
the design space was not required, the simulations were con-
ducted using a constant vertical load rather than a prescribed
vertical penetration depth. The load for each tire was chosen
as the static vertical load when the aircraft was decelerating at
10 ft/s2. Because the load was prescribed, the tire penetrated
to a steady-state depth that varied depending on the arrestor
bed material properties.
After experimenting with several methods, the sequence
illustrated by Figure 12-6 proved superior on the basis of pro-
viding the most consistent results with the shortest settling
time. The settling time refers to the second time stage, lead-
ing up to the steady-state rolling behavior when the load
measurements on the tire are recorded.
Motion damping became one of the main problems with
the combined model, tending to control how long the simu-
lation had to run before the model approached steady-state.
Figure 12-2. Depth-varying profiles considered. Two types of motion required damping: (1) oscillations in the
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SPH Arrestor Bed Deformable FEM Main Gear Tires
Constructed with Stratified for B737-800 and CRJ-200
Layering
Models Constructed Using Half-
Deeper Material Becomes
Symmetry
Harder
Figure 12-4. Depth-varying arrestor and tire model.
Top-Most Layer
30 in. 8 Layers
2-In. Particles
36 in.
Figure 12-5. Sectional view of eight-layer arrestor bed model.
tire itself as it rebounded outward and inward from the axle simulation times short. Depending on the strength of the
line, and (2) vertical oscillation of the axle. Properly imple- arrestor material, the simulation time required for settling
mented damping prevented over- and under-damping the could still vary considerably.
solution, leading to the shortest available run time while not
altering the overall response of the system.
12.3.3. Batch Simulations
The final method involved a vertical damping value that
produced slight overshoot behavior. Using this approach Using the arrestor bed model, large batches of simulations
ensured that the full depth had been reached, while keeping were conducted to generate metamodels for studying the
effects of depth-varying material properties. For each tire, the
Table 12-1. FEM tire library for glass foam run sets had three open variables:
arrestor models.
· Bed depth, in incremental depths from 18 to 30 in.;
Aircraft Landing Gear Tire Designation Included in
Evaluation · Material Initial Strength, which defined the compressive
CRJ-200 Main Gear H29x9.0-15 Included
strength at the surface of the bed; and
· Material Strength Gradient, which defined how rapidly the
Nose Gear R18x4.4 -
strength of the material increased with depth (the quadratic
B737-800 Main Gear H44.5x16.5-21 Included
or linear coefficient of the material profile curve).
Nose Gear H27x7.7-15 -
B747-400 Main Gear H49x19-22 -
The large batch simulations were conducted using
Nose Gear H49x19-22 - LS-OPT. Based on the initial model files, LS-OPT generated
