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118 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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119 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- 188.8.131.52. 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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120 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 184.108.40.206. 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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121 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 220.127.116.11. 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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122 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 18.104.22.168. 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 22.214.171.124. 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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123 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 126.96.36.199. 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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124 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 188.8.131.52. 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