Development of an Air Gun Simulation 

Model Using LS-DYNA 

by Mostafiz R Chowdhury and Ala Tabiei 

ARL-TR-3016 July 2003 

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[ Final 11 June 2002-30 September 2002 

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Development of an Air Gun Simulation Model Using LS-DANA 

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MostafE R. Chowdhury and Ala Tabiei* 

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14. ABSTRACT 

This report presents an analytical methodology to simulate the dynamic impact response of a generic artillery component 

subjected to launch simulation in an air gun test environment. An air gun test provides an efficient and effective launch 

simulation platform designed for testing suitability and survivability of future artilleries or projectile components during their 

developmental stage. Lagrangian and Aribitrary Lagrangian/Eulerian methods are used to simulate the impact mitigation 

environment in which the kinetic energy of a projectile is absorbed by crushing aluminum (Al) honeycomb mitigator. Issues 

related to the effectiveness of these methods in simulating a high degree of distortion of Al honeycomb mitigator using the 

available LS-DANA material models 126 (metallic honeycomb) and 63 (crushable foam) are discussed. Both computational 

methods lead to the same prediction for the deceleration of the test projectile and are able to simulate the behavior of the 

projectile. Good agreement between the test results and the predicted projectile response is achieved using the presented 

models and the methods employed. Development of such a simulation code significantly enhances the U.S. Army Research 

Laboratory’s capability in addressing the customer’s need in explaining projectile behavior during an air gun test and is useful 

in facilitating design and preparation of an effective air gun test. 

15. SUBJECT TERMS 

air gun simulation, Al honeycomb mitigator, Lagrangian/Arbitrary Lagrangian-Eulerian FE method, correlation, LS-DYNA, 

gun launch simulation 

16. SECURITY CLASSIFICATION OF: 

17. LIMITATION f0. NUMBER 

OF ABSTRACT OF PAGES 

a. REPORT b. ABSTRACT c. THIS PAGE 

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL 52 

19a. NAME OF RESPONSIBLE PERSON 

Mostafiz R. Chowdhury 

19b. TELEPHONE NUMBER (hchde area code) 

301-394-6308 

Standard Form 298 (Rev. S/BE) 

Prescribed by ANSI Std. 239.18 

ii 
Contents 

List of Figures iv 

List of Tables V 

Acknowledgments vi 

Summary 1 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

Introduction 3 

Objective 4 

Air Gun Test Description 4 

Material Models 8 

4.1 Material 126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 

4.2 Material 63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 

4.3 Material Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 

The FE Model 17 

5.1 LagrangianModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

5.2 ALE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 

Simulation Results 21 

6.1 Lagrangian Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

6.1.1 Material 126 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 

6.1.2 Material 63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

6.2 ALE Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 

Model Validation: Simulation vs. Experiment 36 

Physical Interpretations Using the FE Results 40 
9. Conclusions 40 

10. Recommendations and Significance of the FE Model 42 

11. References 43 

List of Figures 

Figure 1. Schematic of a typical air gun test setup ......................................................................... 5 

Figure 2. A preshot arrangement in the 4-in air gun test . ............................................................... 5 

Figure 3. A postshot configuration of interacting components in a 4-in air gun test. .................... 6 

Figure 4. A postshot view of an Al crushed mitigator.. .................................................................6 

Figure 5. An instrumented test projectile.. .....................................................................................8 

Figure 6. OBR assembly process for the test projectile.. ...............................................................9 

Figure 7. Air gun test results, top accelerations.. .........................................................................10 

Figure 8. Normalized load-displacement of Hexcel38 pcf compressed statically in the axial 

direction (I). ............................................................................................................................. 13 

Figure 9. A confined high strain rate test of the Hexcel38 14 ft./s in the axial direction (I). .... ..14 

Figure 10. Material 126 input parameters .................................................................................... .15 

Figure 11. Material 63 input parameters....................................................................................15 

Figure 12. Stress-strain curves for materials 126 and 63, 90% compaction.. .............................. .16 

Figure 13. Stress-strain curves for materials 126 and 63, 64% compaction.. .............................. .16 

Figure 14. Stress-strain curves for material 126 with strain rate effect. ...................................... .17 

Figure 15. The Lagrangian FE model. .........................................................................................I9 

Figure 16. The ALE model. .........................................................................................................20 

Figure 17. Section cut view of ALE model. ................................................................................ .20 

Figure 18. Material 126 impact simulation,................................................................................ .22 

Figure 19. Material 126 impact simulation, closeup view.. ......................................................... .22 

Figure 20. Energy balance, material 126 ..................................................................................... .23 

Figure 21. Contact force (OBR and mitigator), material 126 ....................................................... 23 

Figure 22. Displacement of the MEM, material 126. .................................................................. .24 

Figure 23. Nodal ID for velocity and acceleration output. .......................................................... .24 

Figure 24. Velocity of OBR, material 126 .................................................................................... 25 

iv 
Figure 25. Acceleration of four nodes on the OBR, material 126. .............................................. .25 

Figure 26. Acceleration of a top node on the OBR, material 126 ................................................ 26 

Figure 27. Acceleration of the top of the OBR filtered at 2500 Hz, material 126.. ..................... .26 

Figure 28. Displacement of the OBR for two different efficiencies of material 126. .................. 27 

Figure 29. Acceleration of the top of the OBR for two different efficiencies of material 126.....2 7 

Figure 30. Crushed mitigator, material 63 .................................................................................... 29 

Figure 3 1. Velocity of several nodes on the OBR, material 63. ..................................................29 

Figure 32. Acceleration of several nodes on the OBR, material 63 . ............................................ 30 

Figure 33. Acceleration of the top of the OBR filtered at 2500 Hz, material 63 .......................... 30 

Figure 34. Acceleration of the top of the OBR using materials 126 and 63 ................................. 31 

Figure 35. Volume fraction of the mitigator at time zero ............................................................. 32 

Figure 36. Volume fraction of the mitigator at the end of the simulation...................................32 

Figure 37. Locations of the nodal point for kinematics output.. .................................................. .33 

Figure 38. Velocity of the OBR as a function of time .................................................................. 33 

Figure 39. Acceleration of several nodes on the OBR .................................................................. 34 

Figure 40. Acceleration of the top of the OBR.. ..........................................................................34 

Figure 41. Acceleration of the top of the OBR filtered at 2500 Hz.. ........................................... .35 

Figure 42. Acceleration of the top of the OBR filtered at 2500 Hz for both the Lagrangian 

and ALE simulations ...............................................................................................................35 

Figure 43. Top acceleration of the OBR ....................................................................................... 37 

Figure 44. Top acceleration of the OBR filtered at 2500 Hz.. .....................................................37 

Figure 45. Acceleration of the top of the OBR, simulation vs. experiment . ................................ 38 

Figure 46. FFT of the experiment and simulation results ............................................................. 38 

Figure 47. Simulation vs. experiment, acceleration of top of OBR filtered at 7000 Hz...............3 9 

Figure 48. Simulation vs. experiment, acceleration of top of OBR filtered at 2500 Hz...............3 9 

Figure 49. Plots of relative displacements for different parts of the air gun apparatus.. ............ ..4 1 

List of Tables 

Table 1. Basic physical data for the air gun test. ...........................................................................9 

Table 2. Sample statistics of ALE (coarse mesh) and Lagrangian (fine mesh) models. ............ ..17 
Acknowledgments 

The analytical work presented here was accomplished under a contract (Contract no. DAADl9- 

02-D-0001, TCN 02-125) with the Scientific Services Program (STAS), U.S. Army Research 

Office, Research Triangle Park, NC. Air gun tests were conducted by Ara Abrahamian, U.S. 

Army Research Laboratory (ARL), Weapons and Materials Research Directorate (WMRD), 

Adelphi, MD. Contributions of At-a Abrahamian, Edward Szymanski, and William McIntosh of 

WMRD, ARL in delivering the air gun test are greatly appreciated. 
Summary 

This report presents an analytical methodology to simulate the dynamic impact response of a 

generic artillery component subjected to launch simulation in an air gun test environment. An air 

gun test provides an efficient and effective launch simulation platform designed for testing 

suitability and survivability of future artilleries or projectile components during their 

developmental stage. LS-DYNA models are developed to simulate the impact mitigation 

environment in which the kinetic energy of a projectile is absorbed by crushing aluminum (Al) 

honeycomb mitigator. Two computational methods are used for the simulation: Lagrangian and 

Aribitrary LagrangianEulerian (ALE). This report discusses the advantages, disadvantages, and 

the effectiveness of these methods in simulating a high degree of distortion of Al honeycomb 

mitigator. Both computational methods lead to the same prediction for the deceleration of the 

test projectile. The Lagrangian method is simpler to set up, postprocess, and requires less 

computational time than the ALE method. However, it requires significant expertise to make the 

simulation numerically stable. On the other hand, the ALE method is more diffkult to set up, 

postprocess, and requires much more CPU time. An ALE simulation is more suitable for very 

large deformation problems such as those involving material flow. 

The Al honeycomb mitigator is modeled using two material models available in LS-DYNA 

simulation code. Both material models 126 (metallic honeycomb) and 63 (crushable foam) lead 

to reasonable predictions and are able to simulate the behavior of the projectile. The strain rate 

sensitivity is found to be an important factor in these simulations. Good agreement between the 

test results and the predicted projectile response is achieved using the presented models and the 

methods employed. Development of such a simulation code significantly enhances the U.S. 

Army Research Laboratory’s (ARL’s) capability to address the customer’s need in explaining 

projectile behavior during an air gun test and is useful in facilitating design and preparation of an 

effective air gun test. 

1 
2 
1. Introduction 

APL’s air gun facility has been used widely for testing suitability and survivability of future 

artilleries or projectile components during their developmental phase. An air gun test provides 

an efficient and effective launch simulation platform in which the shock phenomena in a real gun 

test are replicated in a controlled environment. The primary focus of such an air gun mitigation 

test is to simulate a transient shock environmenthat the test item is anticipated to sustain in an 

actual field test. Proper simulation of the gun launch environment using an air gun test, thus, 

demands that the dynamics of the physical energy-absorbing interfacing components that 

regulate the shock environment are properly understood. Currently, a rigid-body simulationbased predictor-corrector approach is used for selecting physical operating parameters in an air 

gun test. Physical design parameters are selected such that a target deceleration profile is 

attained during the gun launch simulation test. A rigid-body simulation-based approximate 

selection procedure fails to capture the dynamics of the projectile because of its innate 

simplifications. Development of a virtual simulation model capable of including gun launch 

dynamics is, thus, deemed essential in advancing APL’s air gun test capabilities and in meeting 

the customer’s ever-increasing demand. This methodology requires developing a predictive 

model of responses of the test article. This report presents the development of a finite-element 

(FE) model to simulate the dynamic impact response of a generic artillery component mounted 

on a given projectile during gun launch simulation in an air gun test. 

Several LS-DYNA models of a generic test article fired in a 4-in air gun chamber are developed 

in this study. Control test data for a test item mounted on a projectile are used for model 

validation and correlation. Analytical simulation of the air gun launch environment requires the 

modeling of an event in which the test object mounted on a projectile is launched and decelerated 

by crushing the Al honeycomb mitigator in the recovery chamber. As a secondary energy 

absorbing device, a momentum exchange mass (MEM) is used at the retrieving end. Two 

formulations are used in the simulations: Lagrangian and ALE. The Al honeycomb mitigator 

undergoesignificant deformation that could render a severely unstable Lagrangian simulation. 

For this reason, an ALE simulation is also considered. The Eulerian method is more suitable for 

problems involved in severe mesh distortion. The Lagrangian method, on the other hand, is 

limited in how much an element can deform. The Lagrangian method is easy to set up and 

visualize since the material point moves with the mesh. The Eulerian method, however, is more 

difficult to set up, and the mesh is stationary so that material points are advected (flowed) from 

one element to the next. 

The Al honeycomb mitigator is modeled with *MAT-MDIFIED-HONEYCOMB in the 

LS-DYNA simulation code. This is material model 126 in the code. This material model is 

available for the Lagrangian method only and it is not yet implemented in the Eulerian solver 

3 
of the LS-DYNA. Therefore, an alternative material model is considered that can simulate the 

behavior of Al honeycomb and is available in the LS-DYNA Eulerian solver. The material 

model considered for this case is *MAT-CRUSHABLE-FOAM, which is material model 63 in 

LS-DYNA. This material model can simulate an isotropic crushable material, while the 

*MAT MDIFIED HONEYCOMB can simulate orthotropic crushable material. Most of the Al - 

honeycomb materi. in the air gun simulation is crushed axially. Therefore,, the 

*MAT CRUSHABLE FOAM model is considered to be appropriate for this model. The two - - 

material models are described in detail in section 4. 

2. Objective 

The objective of this effort is to cfevelop an updated and correlated analytical model to predict 

three-dimensional (3-D) transient response of a generic artillery component subjected to launch 

simulation in the ARL 4-in air gun facility. The simulation is achieved using impact mitigation 

techniques, whereby the component is propelled to a target inside a 4-in carrier equipped to 

measure component response during the simulation. The overall model includes all elements of 

the simulation apparatus that contribute to the total response of the test item carried by the air 

gun projectile during its course through its flight. 

3. Air Gun Test Description 

A schematic diagram for a typical air gun test setup is shown in Figure 1. The test setup consists 

of a stationary gun barrel, a projectile, and a dual energy-absorbing mechanism consisting of a 

mitigator and a MEM positioned at the recovery end. In a typical air gun mitigation test, the 

projectile-carrying the artillery components to be tested-is launched to impact an Al 

honeycomb mitigator at the recovery chamber. On impacting the mitigator, the kinetic energy of 

the projectile is lessened by crushing the Al honeycomb mitigator. Crushed mitigator in turn 

exchanges its momentum to a MEM, a secondary energy-absorbing device, abutting its rear end. 

A preshot arrangement of the dual energy absorbing devices in a 4-in air gun retrieving chamber 

is shown in Figure 2. As seen in the figure, the mitigator is stationed inside the split catch tube at 

the start of the test. The steel catch tube for the 4-in gun is 21 in long having an inner diameter 

(ID) of 4.025 in and an outer diameter (OD) of 6.062 in. Four 12.7~mm (0.5-h) diameter, 4340 

steel tie rods (two on each side of the aisle, Figure 2) are used to fasten the top-half of the split 

catch tube with the stationary bottom-half shown in the figure. Bolts are 88.9 mm (3.5 in) from 

the ends of the catch tube. The striking end of the 0.6087 g/cm3 (38 pcf) Al honeycomb 
Gun Barrel 

4-in diameter 

Al Honevcomb Mitigator 

. On-board recorder (OBR) Momentum Exchange Mass (MEM) 

. Test item is mounted on OBR case n 4240 steel 

. see Table 1 

Air gun max velocity -1200 fps for a loo-lb projectile 

Figure 1. Schematic of a typical air gun test setup. 

Figure 2. A preshot arrangement in the 4-in air gun test. 

5 

mitigator was fashioned to form two sharp wedges. With two such wedges at the striking end, 

the mitigator tends to crush evenly across its face. The length of the wedges also determines the 

projectile’s deceleration profile during the impact. On initiation of an air gun shot, the test 
projectile is launched from the breech chamber and is retrieved in the recovery chamber. A 

postshot relative position for the physical apparatus is shown in Figure 3. As seen in this figure, 

on hitting its target, the projectile remains trapped in the catch tube, the mitigator crushes, and 

the MEM displaces. An enlarged view of the crushed mitigator and the undeformed test 

projectile is shown in Figure 4. 

Figure 3. A postshot configuration of interacting components in a 4-in air gun test. 

Figure 4. A postshot view of an Al crushed mitigator. 
A test projectile-consisting of a rectangular Al plate mounted on the top of an on-board 

recorder (OBR) case-was specially prepared for FE verification. The projectile included the 

OBR carrier and a rectangular plate mounted on its top. In this test projectile, the OBR records 

the data and the plate is the test item, representing a simulated projectile component that could be 

used in an actual air gun test. The following are basic dimensions for the test projectile: 

. Outer diameter = 101.09 mm (3.98 in), 

l Inner diameter = 75.95 mm (2.99 in), 

l Length = 152.4 mm (6 in), 

l Wall thickness = 12.7 mm (0.5 in), 

l End cap thickness = 25.4 mm (1 in), 

l Top cap thickness = 12.7 nnn (0.5 in), and 

l Test plate dimension: 101.0 mm (4 in) x 76.2 mm (3 in) x 12.7 mm (0.5 in) Al plate, 

mounted on top cap. 

Figure 5 shows the test projectile and the instrument locations for which the data were recorded 

using an on-board 12-bit, 4-channel high shock analog recorder placed inside the OBR case. 

Two accelerometers and two strain gages were mounted on the test item. The analog recorder 

was shock isolated inside the canister by suspending the device over glass beads and densely 

packed once the top mount had been assembled. Figure 6 shows the OBR assembly process for 

the test projectile. Packing the recorder with glass beads was an effective filtering mechanism in 

arresting propagation of the high-frequency shock wave from the container to the analog 

recorder. An isolated packaging arrangement was needed to ensure that the sensor data recorded 

during the flight were not contaminated by the recording device’s own dynamics and also to 

ensure survival of the OBR. 

Test data for three air gun shots were recorded in this study for subsequent FE model validation 

and verification purposes. Basic physical data for the recorded test shots are presented in 

Table 1. As indicated in the table, relative changes in the properties of the mitigator can 

substantially change the dynamic event of the air gun test. Shot 3, for example, was severe in its 

action and broke one of the tie rods that connected two halves of the catch tube, and the mitigator 

crushed the most. Filtered acceleration history for the top accelerometer for each shot is 

compared in Figure 7. Maximum peak acceleration for these shots ranged from 17,000 to 

18,000 g’s, where g is the acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2). 
4. Material Models 

The two material models considered here are materials 126 and 63 in LS-DYNA. The 

formulations of the two material models are described in detail in the following subsections. The 

input required for the two material models are described as well. 

One of the most difficult aspects of this investigation was to define the material properties that 

would representhe physical behavior of the Al honeycomb mitigator used in the air gun test. In 

this investigation, no test was conducted for characterizing mitigator properties. Therefore, it 

was required to depend on the data available in the open literature. An experimental 

characterization of Al honeycomb material reported by Lu and Hinnerichs (I) was similar to the 

one that was used in this investigation. The crush test results available (I) were used to construct 

the material model used in the air gun simulations. 
(a) OBR Device (b) Glass Beads Filled 

(c) Fabricated Assembly 

Figure 6. OBR assembly process for the test projectile. 

Table 1. Basic physical data for the aim r gun test. 

Mitigator weight, g 

Mitigator crashed length, in 8.28 6.9 3.98 

Wedge depth, in 1.5 1.5 1.5 

No. of wedge peaks 2 2 2 

Maximum acceleration, kg -17 -18 -17 

No damage to the catch One of the 0.5~in tie rods 

Posttest remarks tube No damage broke, and the top-half of 

the catch tube flew awav 

9 
20,000 

15,000 

Bm 

; 10,000 

‘r; 

5,000 

0 

0 

T 

-.__ 

-SHOT-l Lowpass filter 

Figure 7. Air gun test results, top accelerations. 

4.1 Material 126 

This material model is suited to model metallic honeycomb (2-f). The behavior before 

compaction is orthotropic where the components of the stress tensor are uncoupled, i.e., a 

component of strain will generate resistance in the local a-direction with no coupling to the local 

b and c directions. The elastic modulii vary Corn their initial values to the fully compacted 

values linearly with the relative volume: 

where 

P=max 

,( 1: 

min I-’ ----,I 30 l-V, 

and G is the elastic shear modulus for the fully compacted honeycomb material: 

The relative volume, V, is defined as the ratio of the current volume over the initial volume, and 

typically, V = 1 at the beginning of a calculation. 

10 
At the beginning of the stress update, we transform each element’s stresses and strain rates into 

the local element coordinate system. For the uncompacted material, the stress components are 

updated using the elastic interpolated modulii according to the following: 

We then independently check each component of the updated stresses to ensure that they do not 

exceed the permissible values determined from the load curves, e.g., if 

Jay;+l~q > a&) (5) 

then 

(6) 

The components of aii (Ed) are defined by load curves. 

The material model requires the stress vs. strain curve to be supplied. The strain for this material 

model must be input as logarithmic strain (5). Therefore, the experimental data which are given 

in terms of engineering strain must be converted. The relation between the engineering strain, e , 

and the logarithmic strain, E , is as follows: 

where the engineering strain, e , is defined by the following equation: 

L-L, _ L e=-- pi. 

Lo 0 0 

(8) 

For instance, if the efficiency of the honeycomb material is 90%, the material final length is only 

10% of its initial length. The logarithmic strain in this case is 

E = Zn(l g I) = 2.3026. 

I I . 

(9) 

4.2 Material 63 

This material model is suited for modeling crushable foam (2-4). This isotropic foam model 

crushes one-dimensionally with a Poisson’s ratio that is essentially zero. In the implementation, 

we assume that Young’s modulus is constant and update the stress assuming elastic behavior: 

11 
The magnitudes of the principal values o,?‘, i = 1,3 are then checked to see if the yield stress 

LT, is exceeded; ifso, they are scaled back to the yield surfaces such that if 

0)) < qP’ I I (11) 

then 

After the principal values are scaled, the stress tensor is transformed back into the global system. 

The material model requires the stress vs. strain curve to be supplied. The strain for this material 

model must be input as volumetric strain (5). Therefore, the experimental data which are given 

in terms of engineering strain must be converted. The volumetric strain, E, , is defined as 

follows: 

Since we can assume that the crushable foam is crushed under a very small Poisson’s ratio, the 

initial cross-sectional area is the same as the final one. Therefore, in this case the volumetric 

strain can be simplified as follows: 

L E, =l--. 

Lo 

(14) 

For instance, if the efficiency of the honeycomb material is 90%, the material final length is only 

10% of its initial length. The volumetric strain in this case is 

g, =1-L+%o.go. 

L, 1.0 (15) 

4.3 Material Parameters 

Mechanical compressive load carrying behavior for an Al mitigator can be described using the 

normalized load-deflection profile shown in Figure 8. As seen in the figure, three distinct 

features characterize the honeycomb mitigator’s load carrying behavior. These features include 

linear elastic tendency up to initial crushing, typical volumetric crush, and final phase hardening 

12 
Linear elastic 

0.0 0.2 0.4 0.6 0.8 

Figure 8. Normalized load-displacement of Hexcel38 pcf compressed statically in the axial direction (I). 

to full compaction. Almost all energy absorption is done in the volumetric crush zone. Initial 

spikes at the end of linear behavior are typical in Al honeycomb resistance profile and can be 

elirninated by crushing the striking edge of the mitigator. The fluctuation of strength during 

volumetric crushing, as seen in the figure, may have resulted by instability due to buckling of 

honeycomb cells. 

Six honeycomb specimens (Hexcel38 pcf) were tested statically by Lu and Hinnerichs (I). 

Compression tests for these specimens were performed along the principal material direction. 

Figure 8 shows the compression results. A confined compression test was also conducted by Lu 

and Hinnerichs (I), and the results are depicted in Figure 9. The rate of loading used is 

4267 nun/s (14 fVs). The solid line in Figure 9 is the stress-strain curve obtained from the 

dynamic test while the dotted line represents the average behavior. In the figure, the three zones 

are clearly shown and are the ones used in determining the material parameters needed by 

materials 126 and 63 in LS-DYNA. 

Material parameters that are needed for FE material models are derived from the loaddisplacement curve described in Figure 8. The dynamic crush strength, however, increases with 

higher impact velocity, which must be accounted for in the material formulation (6). Parameters 

of interest for the material model include the following: crush strength, crush efficiency 

(volumetric strain that initiates the hardening), hardening modulus, and strain rate enhancement 

due to increase in impact velocity. Jn this investigation, a stress scale factor (relative increase in 

strength due to impact velocity) is used because of the unavailability of high strain rate 

dependent experimental data. A range of stress scale factor, suggested by Bitzer (6), is studied to 

determine the sensitivity of such parameters in governing the dynamics of the projectile model. 

13 
16 

. . _ . , I . . ‘““~“” 

j Average Crush Strength: 

_..._ -.._ _ .. . . ..-... _~ ..-.. _ .. . . ?-...- .._......_..... i .. . . 

: Crush Efficiency: 

. . . . . . . i . . . . ..~..._...._ j . . .._.._.. . i . . . .._..........._. / .__.__.._.......__._ i ._____ ,.__,_..._. !.. .___..._,___.__.._ i lll1(1111 ,,,I 

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 

AL/L, 

Figure 9. A confined high strain rate test of the Hexcel38 14 ft/s in the axial direction (I). 

Figures 10 and 11 report the material parameters extracted from the tests and used in 

LS-DYNA’s *MAT-MODIFIED-HONEYCOMB and *MAT-CRUSHABLE-FOAM material, 

respectively. Two sets of load curves are used in the material models. One is for 90% 

compaction and the other is for 64% compaction. Lu and Hinnerichs (I) report that the material 

efficiency is 64% and full compaction is at 78%. 

In order to verify the validity of the previously mentioned materials models, an FE model was 

developed to simulate the compression test reported by Lu and Hinnerichs (I). The displacement 

control is used in the simulation. The stress-strain curve for the case of 90% compaction is 

shown in Figure 12 for both material models (126 and 63). A 90% efficiency means that the 

final length is only 10% of its initial length. Figure 13 depicts the stress-strain curves for the 

case of 64% compaction for both material models. Material 126 has a strain rate effect 

algorithm. The strain rate effect is activated by the seventh material parameter on the first control 

card in the material model. The strain rate parameter’s function is to shift the stress value above 

the static values as determined by the material parameters in the material model. A simulation is 

performed in which the average strain rate is 50 mm/mm/s, and the strain rate parameter used in 

the model is 100. Figure 14 depicts the stress-strain curve for the static and rate sensitive cases. 

One can observe that for this case, the rate sensitive stress is about two times the static stress. 

This simulation testifies to the effectiveness of the proposed material models in simulating the 

mean load-displacement relationship of the Al honeycomb mitigator. This material model, 

however, disregards the strength fluctuation that exists in physical tests (see Figure 8). 

14 
$---+----l--w- + ---- 2 ---- + _--- 3 ---- + --__ 4 ____ + ____ 5 ____ + ____ 6 ____ + ____ 7 ____ + ____ 8 

*MAT-MODIFIED-HONEYCOMB 

2 l.OOOE-104.060E+03 0.0000 5.588E+Ol l.OOOE-03 l.Oe-9 

66.0 66.0 66.0 66.0 0.0 0.0 0.0 0.0 

4060.00 4060.00 4060.00 2028.0 2028.0 2028.0 0.0 

O.OOOE+OO O.OOOE+OO O.OOOE+OO O.OOOE+OO O.OOOE+OO O.OOOE+OO 

O.OOOE+OO O.OOOE+OO O.OOOE+OO O.OOOE+OO O.OOOE+OO O.OOOE+OI 

O.OOOE+OO 

*DEFINE-CURVE 

66 

0.00500000E+00 13.750 

0.02000000E+00 55.160 

2.3026 60.000 

3.00000 40.60e2 

*DEFJNE CURVE 

661 - 

0.00500000E+00 13.750 

O.O2OOOOOOE+OO 55.160 

1.02170 60.000 

3.00000 40.60e2 

$---+----l----+----2----+----3 ---- + --__ 4 ____ + ____ 5 ____ +---~6 ____ + ____ 7 ____ + ____ 8 

Figure 10. Material 126 input parameters. 

$-+ ____ I_--_ + ____ 2 ____ + ____ 3 ____ + ____ 4 ____ + ____ 5 ____ + ____ 6 ____ + ____ 7 ____ + ____ 8 

*MAT CRUSHABLE FOAM 

l-l.OE-10 4060,OO 0.000 67 l.Oe-9 

*DEFINE-CURVE 

671 

O.OO5OOOOOE+OO 13.750 

0.02000000E+00 55.160 

0.90 60.000 

0.99000000E+00 40.60e2 

*DEFINE-CURVE 

67 

O.OO5OOOOOE+OO 13.750 

O.O2OOOOOOE+OO 55.160 

0.64 60.000 

O.99OOOOOOE+OO 40.60e2 

$-em+ ---- I_--- + --__ 2 ___- + ____ 3 ____ + ____ 4 ____ + --_- 5 ____ + ____ 6 ____ + ____ 7 ____ + ____ 8 

Figure 11. Material 63 input parameters. 

15 
5OO mat 126 and 63 with 90% efficiency 

3 

&mat 126 

..a mat63 

X-strain 

Figure 12. Stress-strain curves for materials 126 and 63,90% compaction. 

,ooo mat 126 i 

800 

d 63 efficiency 64% 

- 

A .B ____... A ___. ..B ____.._... -- ,..L. ^- A... 

I I I I I O-4 O-6 0.8 

lbmat12E 

8 mat63 

Figure 13. Stress-strain curves for materials 126 and 63,64% compaction. 

16 
2oo Average strain rate is 50 mrrdmrdsec 

150 

&static 

+phin 

0 

0 0.5 1 1.5 2 2.5 3 

X-strain 

rate 

Figure 14. Stress-strain curves for material 126 with strain rate effect. 

5. The FE Model 

Four FE models were developed in this investigation. Two models are used in the Lagrangian 

simulations and two are used in the ALE simulations. The two sets are coarse and fine mesh. 

The two simulation methods are used and considered since it is anticipated that the Lagrangian 

simulation is unstable due to large deformation of the Al honeycomb. Lagrangian descriptions 

of material have limitations for severe mesh distortion. On the other hand, the Eulerian 

description of material is more stable under large deformation since the material is assumed to 

behave like fluid. In the next sections, a description of the two methods are presented in detail. 

Sample statistics on the Lagrangian and ALE methods are shown in Table 2. The statistics 

shown in this table are for computer runs that were conducted on an ARL high performance 

computer SGI Origin 2000* server system. 

Table 2. Sample statistics of ALE (coarse mesh) and Lagrangian (fine mesh) models. 

Parameter 

No. of nodes 

No. of elements (brick, beam, and shell) 

Total execution time, ms 

Time step, s 

CPU time, s 

FE Model 

ALE Lagrangian 

69,578 118,842 

65,724 123,164 

5 3.5 

8.29e-8 to 1.20e-7 1.90e-7 to 1.72e7 

262,292 43,408 

* SGI Origin 2000 is a registered trademark of Silicon Graphics Inc. 

17 
5.1 Lagrangian Model 

The FE model of the Lagrangian test setup is depicted in Figure 15. The model consists of the 

catch tube (wired mesh), the OBR (brown mesh), the instrumented plate (dark blue mesh), the 

MEM (yellow mesh at the rear end), and four beam elements that represent the bolts connecting 

the two halves of the catch tubes. On modeling the OBR, no inner filler materials including the 

recording devices and the glass beads (Figure 6) were included in the FE model. The total mass 

of the instrumented OBR was simulated in the FE model by adjusting the density of the OBR 

canister. The analytic simulation of the impact starts with an initial input velocity for the 

projectile from the position shown in the figure. The initial velocity was obtained by double 

integrating the recorded accelerometer data from the actual test shot. As seen in the figure, the 

initial velocity of the projectile at its impact was -83,566 mm/s (3290 in/s). 

The fine mesh model is used for generation of the simulation results and the experimental 

comparison. The fine mesh model consists of 118,842 nodes and 123,164 elements. There are 

14,744 shell elements, 108,416 solid elements, and 4 beam elements in the model, Several 

contact surfaces are defined in this model. A contact surface is defined between the OBR and the 

mitigator, the OBR and the catch tube, the mitigator and the catch tube, and the mitigator and the 

MEM. The segment-based contact is used in this case, which proved to be more stable. Two 

material models in the LS-DYNA simulation code are considered in this model: 

*MAT MODIFIED HONEYCOMB and *MAT - - - CRUSHABLE-FOAM. 

5.2 ALE Model 

Since it is difficult to simulate very large deformation in the Lagrangian method easily, the ALE 

method is employed. The Lagrangian method requires significant expertise in modeling severe 

deformation. The ALE method, on the other hand, is more stable for such problems. Two 

models are developed here as well: a coarse and a fine mesh. The coarse mesh model is 

employed for generation of the simulation results. The fine mesh model led to a very small time 

step which rendered the simulation computationally inefficient. The coarse mesh model 

consisted of 69,578 nodes and 65,724 elements. There are 4440 shell elements, 61,280 solid 

elements, and 4 beam elements in the model. The ALE finite element model is depicted in 

Figure 16. The model consists of the catch tube, the OBR (glass beads are not modeled as in 

Lagrangian case), the instrumented plate, and the MEM that is similar to the Lagrangian model. 

The mitigator, however, is modeled differently here. The mitigator is a model with solid element 

formulation no. 12 in LS-DYNA. This element formulation is ALE plus void, where the void is 

the surrounding space in which the distorted material can flow. The mesh in this part does not 

distort, which is the case with the Eulerian description of motion. The mitigator is surrounded by 

void elements. The void element is there for the possibility of the mitigator material flow. The 

mitigator material upon deformation can flow outside of the mitigator mesh. Once this happens, 

the mitigator material can flow into the void elements. The solid elements of the mitigator and 

18 
j ...I ‘.. 

- Vel, Trapezoidal i”.kec 

-- l 

Figure 15. The Lagrangian FE model. 

void have node-to-node correspondence at the boundaries. Figure 17 depicts a section cut 

through the middle of the mesh. The blue mesh in this figure represents the mitigator 

honeycomb; the red mesh is the surrounding void. 

The integration time step in an ALE simulation is smaller than a Lagrangian simulation for the 

same mesh size. This is attributed to the way LS-DYNA does the ALE formulation. The 

explicit time integration time step in the Lag-rangian method, in general, is a function of the 

smallest element’s characteristic length and material properties. In the ALE method, in addition to 

that previously mentioned, it is also a function of mesh velocity, i.e., the velocity of the material 

grid as it distorts. Due to this fact, the integration time step in the ALE method is smaller than the 

Lagrangian method. 

19 
Figure 16. The ALE model. 

Figure 17. Section cut view of ALE model. 

20 
6. Simulation Results 

The simulations were carried out on a 1.7~MHz laptop computer and also independently on an 

ARL Major Shared Resource Center (MSRC) SGI Origin 2000 server system. The duration of 

the impact event was -2 ms. The contact of the OBR with the mitigator lasted only -1 ms. Two 

types of simulations were carried out, namely, Lagrangian and Eulerian simulations. The CPU 

time using the laptop for the Lagrangian simulation was -4 hr. The Eulerian simulation took -16 

hr to complete even though the number of elements is about one-half the Lagrangian simulation. 

The impact velocity in both models is taken as 83,566 mm/s. The three fundamental units used 

here are millimeters, seconds, and metric ton for the length, time, and density, respectively. 

Results of the two simulations are presented next. 

6.1 Lagrangian Simulations 

The Lagrangian simulation was carried out for two different material models in LS-DYNA: 

*MAT MODIFIED HONEYCOMB, which is material 126, and 

*MAT-CRUSHABLE - FOAM, which is material 63. Results of the simulations utilizing both - 

material models are presented next. 

6.1.1 Material 126 

The material parameters used in this model are those listed in Figure 10. The stress values are 

scaled by 1.2 to account for the high-velocity impact. The strain rate effect must be included in 

such a simulation since the material exhibits strain rate sensitivity. However, since experimental 

data for the used honeycomb material under high strain rate are not available, the stresses are 

scaled by a multiplier. The range of stress scale factor used is between 1.2 and 1.5 for this 

material model (6). 

Two different material efficiencies are considered for the simulations: 90% and 64% 

compaction. The 64% efficiency (or compaction) predicted a stiffer response than the 90% 

compaction. Figures 18-27 depict the simulation results for 90% efficiency. Figures 28 and 29 

show the difference in predictions of the two efficiencies. 

Figures 18 and 19 show the impacted geometry and closeup view of the impacted geometry for 

material 126, respectively. Figure 20 depicts the energy balance as predicted by the simulation. 

One can see that the energy is conserved in this simulation, which is an indication of numerical 

stability of the model. The hourglass energy and contact energy (not shown in the figure) is 

much smaller than the internal energy as desired in a stable impact simulation. The contact force 

between the OBR and the mitigator is shown in Figure 21. Figure 22 depicts the displacement of 

the MEM as a function of time. 

21 
r 

Figure 18. Material 126 impact simulation. 

Figure 19. Material 126 impact simulation, closeup view. 

22 
#WL GUN SIMUiATlON 

Component 

AKinetic Energy 

-B-Internal Energy 

Clotal Energy 

-D J-burglass Energy 

FSliding Energy 

Figure 20. Energy balance, material 126. 

AFtl GUN SIMULATION 

contact Id 

Asll 

1 

Time (E-g31 

Figure 2 1. Contact force (OBR and mitigator), material 126. 

23 
Rigid Body Ids 

A4 

I I 

0 OS 1 15 

Time (E-03) 

Figure 22. Displacement of the MEM, material 126. 

Y 

I 

A X 

I 

Figure 23. Nodal ID for velocity and acceleration output. 

J 

24 
. 

2u AKL WJN SlMurAr tON 

I 

lime (E-Q31 

Figure 24. Velocity of OBR, material 126. 

Node Ids 

A!Lll%471 

AL1 18537 

AL118314 

. ..D ,... 118818 

-0.4 f I I I 

Q u-5 1 1.5 

Time (Elt3) 

Figure 25. Acceleration of four nodes on the OBR, material 126. 

25 
-0.4 [ I I I I I 1 

0 0.5 1 1.5 

lime (E-03) 

Awl18818 

Figure 26. Acceleration of a top node on the OBR, material 126. 

-0.05 I I 1 I I I I 1 

0 0.5 1 1.5 

Time (E-03) 

Figure 27. Acceleration of the top of the OBR filtered at 2500 Hz, material 126. 

26 
with 90% eff. 

with 64% :eff. 

AA&it 126 

ELMat 126 

5 1 1.5 

-lime fE-53) 

Figure 28. Displacement of the OBR for two different efficiencies of material 126. 

AM% 

._.. 8! 9B % 

lime [E-03) 

Figure 29. Acceleration of the top of the OBR for two different efficiencies of material 126. 

27 
To compare simulation responses to that of the experimental tests, several modal locations were 

selected for kinematics output. The locations of these nodes were the same locations on the 

OBR in the experimental tests. These locations are shown in Figure 23. The velocities of the 

selected nodes are shown in Figure 24. Figure 25 depicts the acceleration of these nodes. The 

frequency of output is selected to be the same as the one used in the experiments, which is 

4.OE-6 s. The acceleration of the top of the OBR is shown in Figure 26. This acceleration data 

are filtered with a low-pass filter with a cutoff frequency of 2500 Hz and is shown in Figure 27. 

The honeycomb material reported by Lu and Hinnerichs (I) has an efficiency of 64%-78%. The 

simulations indicated that the 64% efficiency model led to a stiffer behavior as far as the 

mitigator crushed distance is concerned. Figure 28 shows the displacement of the OBR for the 

two honeycomb efficiencies considered. One can observe that the 90% honeycomb efficiency 

led to more displacement of the OBR and consequently a greater crushed distance of the 

mitigator. The stress scale factors in these simulations were taken as 1.5. Figure 29 depicts the 

filtered acceleration of the top of the OBR for the two honeycomb efficiencies considered. These 

acceleration data are filtered with the same low-pass filter with a cutoff frequency of 2500 Hz. 

6.1.2 Material 63 

The *MAT-CRUSHABLE-FOAM in LS-DYNA is used in the following simulations. The 

stress is scaled by 1.5 to account for the strain rate sensitivity. The material input data for this 

simulation are reported in Figure 11. 

The CPU time for the simulation using this material model is about the same as material model 

126. The crushed mitigator is shown in Figure 30. The qualitative difference between the 

simulations using materials 63 and 126 was insignificant. Figure 3 1 depicts the velocity of the 

OBR as function of time. Figure 32 shows the acceleration of several nodes on the OBR. The 

frequency of output is the same as the previous material model and the same as the experimental 

data. The accelerations are filtered with a low-pass filter with a cutoff frequency of 2500 Hz and 

shown in Figure 3 3. 

Figure 34 depicts the filtered acceleration of the top of the OBR for material 126 and material 63. 

The magnitude of the acceleration for the two materials is about the same. However, there is 

some difference in the duration of the pulse. This difference is attributed to the differences in the 

formulation of the two material models. The *MAT~MODIFIED~HONEYCOMB is an 

orthotropic material, which assumes that stress components are fully decoupled. Straining of the 

material in the local material axis in one direction causes stress in that direction only. However, 

the *MAT-CRUSHABLE-FOAM is an isotropic material model, and the stress components are 

28 
ARLGUN SIMULATION 

Time = 0.002 

Figure 30. Crushed mitigator, material 63. 

ARlGWN SlMWlATlON 

Node Ids 

-100 I I 1 I 

0 0.5 1 1% 

‘Time (E-03) 

Figure 3 1. Velocity of several nodes on the OBR, material 63. 

29 
ARL GUN SIMULATION 

NodeIds 

A118471 

Al 18537 

Lll8814 

a-1 18818 

0 O-5 1 l-5 

l-me (E-03) 

Figure 32. Acceleration of several nodes on the OBR, material 63. 

0.2. 

0.15, 

B 

& 0.1 

E ‘Xi 

!!? al 0.05 

z 

iii 

I4 

0 

-0.05 

RL GUN SIMUL& 

P” / .’ 

/ 

,,: 

I 

ION 

I 

Y 

i \ 

t D 

\ 

i 

Time (E-03) 

i 

Node Ids 

Al 18471 

wEI-1 18537 

Cl18814 

.Jxl18818 

Figure 33. Acceleration of the top of the OBR filtered at 2500 Hz, material 63. 

30 
Mat 126 Vs- Mat 63 

A&fat 63 

1L.Mat 126 

\ 

4.05, I I I I I I 1 

0 OS 1 1.5 

lime (E-U3) 

Figure 34. Acceleration of the top of the OBR using materials 126 and 63. 

6.2 ALE Simulation 

The mesh is fixed in an ALE simulation. In this situation, one can look at the volume fraction of 

the material. The volume fraction is equal to 1 when the element is filled with the material. 

Volume fraction cl means that only part of the element is filled with the material. The volume 

fraction of the mitigator material at time zero is shown in Figure 35. The volume fraction of the 

mitigator material at the end of the simulation is depicted in Figure 36. One can observe that the 

Eulerian mesh has not moved; however, the material has passed from one element to the next 

indicating material flow and deformation. 

Figure 37 shows locations of several nodal points for kinematics output. The velocity of the 

OBR as a function of time is shown in Figure 38. Acceleration of several nodes on the OBR is 

depicted in Figure 39. The frequency of output is selected to be the same frequency as in the 

experimental tests. The acceleration of the top of the OBR is depicted in Figure 40. These data 

are filtered with a low-pass filter with a cutoff frequency of 2500 Hz and are shown in 

Figure 41. Comparison of the prediction of the acceleration of the top of the OBR using the 

Lagrangian and ALE methods is shown in Figure 42. A small difference is observed in the 

magnitude of the peak acceleration. This difference, however, can be neglected and assumed to 

be a numerical error difference between the two methods. 

31 
FdcqcLw& 

l.oooctoeo - 

9.owrom~ 

t 

X 

4 

Figure 35. Volume fiwtion of the mitigator at time zero. 

yLGwtxldulAnon 

lime= - FhcFigure 36. Volume fiaction of the mitigator at the end of the simulation. 

32 
. 

ML SUN SIMULAION 

lime = 0.0034 

Figure 37. Locations of the nodal point for kinematics output. 

Node Ids 

A6920? 

J-69276 

AL69273 

-a,69554 

A6920? 

,Jw6927U 

Figure 38. Velocity of the OBR as a function of time. 
oe6 ARL GUN SIMUIATION 

Node Ids 

o-4 

A69207 

B-69270 

XL69273 

G D-6!XZi4 

& 0.2 

E 

z 

B 0 

a 

j 

-6.2 

lime (E-63) 

Figure 39. Acceleration of several nodes on the OBR. 

.L _.. 

lime (E-63) 

Figure 40. Acceleration of the top of the OBR. 

34 
. 

Node Ids 

. A69207 

_.. B. . ..fB270 

2269273 

.a69554 

-0.1 I ’ I 0 I I I I I I I I I t 

0 Q-5 1 l-5 2 2-5 3 

Figure 4 1. Acceleration of the top of the OBR filtered at 2500 Hz. 

Lagrangian Vs. ALE Simulatinn 

I 

lime (E-03) 

Figure 42. Acceleration of the top of the OBR filtered at 2500 Hz for both the Lagrangian and ALE 

simulations. 

35 
7. Model Validation: Simulation vs. Experiment 

Several experimental tests were conducted at the ARL air gun facility located at Adelphi, MD. 

The air gun simulation is achieved using impact mitigation techniques whereby the component is 

‘propelled to a target inside a carrier equipped to measure component response during the 

simulation. The initial experimental setup was previously shown in Figure 2. The mitigator is 

placed in the catch tube and in contact with the MEM. The OBR is launched to impact the 

mitigator. Upon crush of the mitigator, it will push and repel the MEM in the opposite direction. 

The postexperiment view was shown in Figure 3. Acceleration data were collected on the top 

and the bottom of the OBR. The acceleration data obtained from the experiment on the top of 

the OBR are reported in Figure 43. This acceleration is filtered with low-pass filter with a cutoff 

frequency of 2500 Hz and shown in Figure 44. 

The simulation results are compared with experiments qualitatively and quantitatively. 

Qualitatively, the deformation of the mitigator looks the same in the simulation and experiment. 

The experimental final crushed length of the mitigator is reported as 210.0 mm (8.27 in). The 

simulated fmal crushed length of the mitigator is predicted to be 226.0 mm (8.90 in), a difference 

of -7% off from the actual crushed length. 

The quantitative validation consists of comparing the acceleration data from simulation and 

experiment. The acceleration of the top of the OBR from simulation and experiment is shown in 

Figure 45. To find out the dominant frequencies in the response of the system the acceleration 

obtained from the simulation is treated with Fast Fourier Transform (FFT). The FFT is 

performed in LSPOST on the acceleration data and shown in Figure 46. One can observe that 

the second dominant frequency for the test spectrum is -7000 Hz. 

For comparison purposes, both the simulation results and the experimental results are filtered 

with low-pass cutoff frequencies of 7000 and 2500 Hz, respectively. The simulations and the 

experiment’s acceleration of the top of the OBR for both filtrations are shown in Figures 47 

and 48. Figure 47 shows a relatively good agreement between the predicted and test acceleration 

responses using material model 126 when a stress scaled factor of 1.5 was used in the analysis. 

A higher stress scale factor (1.5 instead of 1.2) has significantly attenuated the free vibration as 

indicated in Figure 47. Good prediction is observed from the simulation as compared to 

experiment, particularly for the 2500 cutoff frequency. Figure 48 compares several runs for the 

simulation. Two predictions are presented with material 126. The stress is scaled by 1.2 and 1.5 

in the two predictions. One can observe that when the stress is scaled by 1.2, the peak 

acceleration is underpredicted. When the stress is scaled by 1.5, the peak acceleration is 

overpredicted. Figure 48 also shows the prediction of acceleration using material 63, with the 

stress scaled by 1.5 and the same over-predictive trend observed. 

36 
. 

Channel 1 Acceleration Top 

30,000 

25,000 

20.000 

15,000 

10,000 

5,000 

0 

6.0 

-5,000 

-10,000 

# -Channel 1 Acceleration Top 

-02 

Time, BBC 

Figure 43. Top acceleration of the OBR. 

Lowpass filter = 2600 Hz 

Time, see 

37 

Figure 44. Top acceleration of the OBR filtered at 2500 Hz. 
60 Accelerartion top of the OBR 

I 

40 

20 

0 

-20 

Aexperiment 

.Lmat126x1.2 

llmat126x1.5 

0 0.5 1 1.5 2 

Time (E-03) 

Figure 45. Acceleration of the top of the OBR, simulation vs. experiment. 

r of acceleration data 

I 60 

1 

-/MI-test 

&.fft-mat126x1.2 

Ilfft-mat126x1.5 

Frequency (E+3) 

Figure 46. FFT of the experiment and simulation results. 

38 
25 Acceleration of top of OBR filltered at 7000 Hz 

A-test 

&mat1 26x1 .i 

1s ..LLmtl26xl.5 

;;; 15 10 

Y 

g *= 5 

2 al 

2 0 

8 

LJ -5 

-15 I I I I I I 1 

0 0.5 1 1.5 2 

Time (E-03) 

. 

Figure 47. Simulation vs. experiment, acceleration of top of OBR filtered at 7000 Hz. 

Accelerations Fit&wed at 2500 Nz 

2.00E+O4 +- .-..---A 

$OOE+O3 l.... - .._--._.. __-_- -..__.. -. .-.._- -.-...----_-.~ ~_~... .- ..~.. . _ .! 

Time (ms) 

-experiment 

-mat 63 (x1.5) 

Figure 48. Simulation vs. experiment, acceleration of top of OBR filtered at 2500 Hz. 
8. Physical Interpretations Using the FE Results 

FE simulation results help explain the physics of the air gun launch simulation as described here. 

Figure 49 compares the displacement profiles for nodes corresponding to different parts on the 

air gun model. Deflection profile for nodes 118794 and 118259 on the test projectile shows a 

reversal in its motion direction from its highest peak at -0.5 ms. Projectile motion for nodes 

118794 and 118259 closely followed each other as indicated by the overlapping of their histories 

on the top of each other. Mitigator top edge node (77897) followed the deflection profile for the 

projectile nodes (118794 or 118259) until -1 ms. This indicates that the top edge compressed as 

the projectile penetrated the crushing mitigator. At this instant, the energy from the system has 

been transmitted to the MEM, as it gained momentum, and the projectile bounced back. As seen 

in the plots for nodes 77897 and 118259, at -1 .l ms, the mitigator crushed nodes at its tip (node 

77897) did not bounce back as much as did the projectile itself. In essence, the mitigator 

remained in its original position at the end of the gun launch simulation. This phenomenon 

confirms the posttest observation as documented in section 3 (Figure 3). As indicated in the 

figure, the rates and magnitudes of deflections for mitigator nodes (77897, 1708, and 74544) 

starting from its tip of the wedge to the bottom end where the MEM is connected are different. 

The bottom part of the mitigator (node 74544) does not appear to have sensed the motion at least 

until -0.4 ms after the initiation of the impact. The bottom of the mitigator (node 74544) moves 

together with the MEM (node 116926) until 0.9 ms, and then the mitigator starts moving back to 

its initial position. The MEM at this instant gains its momentum and shoots forward until being 

stopped at the rear retrieving end (Figure 3). 

9. Conclusions 

The objective of this effort was to develop an overall analytical model to predict the 3-D 

transient response of a generic artillery component subjected to launch simulation in the ARL air 

gun facility located at Adelphi, MD. The simulation was achieved using impact mitigation 

techniques whereby the component is propelled to a target inside a carrier equipped to measure 

component response during the simulation. Several LS-DYNA models were developed to 

simulate the air gun launch environment in which a test object mounted on a projectile is fired 

through the air gun and decelerated by crushing Al honeycomb mitigator which impacts the 

MEM before being stopped at the retrieving end. Two computational methods are employed for 

this purpose: the Lagrangian and ALE methods. The Lagrangian method is simpler to set up, 

postprocess, and requires less computational time. However, it requires significant expertise in 

the LS-DYNA code to make the simulation numerically stable. This is due to the significantly 

large deformation of the mitigator. On the other hand, the ALE method is more difficult to set 

40 
. 

Relative Displacements of components during air gun simulation 

- OBR Node-l 18794 -m- OBR Node-i 18259 - - - Mitigator Node-l 708 

- - MEM Node-l 16926 e - Mitigator-top NODE 77897 -Mitigator-bottom NODE 74544 

5 

0 

-5 

-10 

-15 

-20 

-25 

1 

I 1’. -4-21 I / I I 

\ mi j 

-30 J ___---- ~I- __-.... -.._ ~-- -_I(__.._.__. _I_~ . ..____ I_lj I 

Figure 49. Plots of relative displacements for different parts of @e air gun apparatus. 

up, postprocess, and requires much more CPU time, but is more suitable for a very large 

deformation-like flow problem. Both computational methods led to the same prediction for the 

acceleration of the OBR. 

Both material models 126 and 63 led to reasonable predictions and are able to simulate the 

behavior of the mitigator. The strain rate sensitivity must be accounted for in these simulations. 

If no strain rate effect is included, the peak acceleration of the OBR is under-predicted. In the 

presented simulation, instead of activating the rate effect in the material models, the stress is 

scaled by values between 1.2 and 1.5. This will have the same effect as if the rate effect is 

activated in the material model. 

Good prediction of the oscillatory characteristics and peak acceleration of the OBR is achieved 

using the presented models and the methods employed. The LS-DYNA simulation code can be 

used for such problems with confidence that the code will aid in prediction of the proper 

response of any instrument mounted on the OBR. 
10. Recommendations and Significance of the FE Model 

Improvements on the LS-DYNA model presented in this report are needed to address its 

limitations and capture the high-frequency transient phenomena that are typical during launchsimulation air gun tests. Once the improvements are incorporated in the current air gun FE 

model, it will significantly enhance ARL’s capability to address the customer’s need in 

explaining projectile behavior during an air gun test and will be useful in facilitating design and 

preparation of an effective air gun test. The following are a few of the suggested improvements 

for the simulation methodology: 

. 

. 

l Investigate damping effect on the response (mass and stiffhess proportional damping) of 

the test article in an air gun simulation test, 

l Characterize material performance for Al honeycomb mitigator from high-rate compression 

test results, 

l Investigate high-frequency contribution on the response of the test article, 

l Develop a roadmap for modeling different gun calibers, and 

l Calibrate FEM with the measured strain data. 

A complementary use of the virtual simulation code could be useful in facilitating design and 

preparation of an effective air gun test. A virtual model could aid in pre- and posttest 

investigation as well. Pretest investigation using an FE model is important in designing and 

selecting proper test configurations and physical operating parameters of an air gun test 

environment. These physical operating parameters include the projectile velocity, the physical 

characteristics of the MEM, and/or the physical characteristics of the mitigator. The ability to 

numerically simulate the dynamic response of the test item will allow the physical operating 

parameters of the air gun test environmento be tuned to achieve the specific dynamic conditions 

that are required for each particular test item. This will significantly reduce the number of test 

results that are deemed unusable due to a failure to meet the required dynamic conditions. In 

addition, it is anticipated that the posttest investigation using the numerical simulation model will 

help explain the source of certain undesirable high-frequency phenomena that are typically 

measured during air gun tests. Furthermore, the full-field results will aid the test designer in 

choosing the optimal locations for the limited number of transducers that can be applied to the 

test item, thereby ensuring that the most useful data are measured in each test. 

. 

42 
11. References 

1. Lu, W.-Y.; Hinnerichs, T.; Crush of High Density Al Honeycombs; Presented at the 

International Mechanical Engineering Congress and Exposition, New York, NY, 

1 l-l 6 November 2001. 

l 

2. Hallquist, J. 0. LS-DIVA Theoretical Manual; Livermore Software Technology Corp.: 

Livermore, CA, 1998. 

3. Hallquist, J. 0. LS-DANA User’s Manual; Liver-more Software Technology Corp.: 

Livermore, CA, 1998; Vol. 1. 

4. Hallquist, J. 0. LS-DIVA User’s Manual; Livermore Software Technology Corp.: 

Livermore, CA, 1998; Vol. 2. 

5. Tabiei, A. Cincinnati, OH. Advanced LS-DYNA Lecture Notes; Livermore Software 

Technology Corp: Liver-more, CA, 1999-2002. 

6. Bitzer, T. Honeycomb Technology; Chapman and Hall: London, UK, 1997. 

43