Technical Report TR–2016–08

NG-NRMM Phase I Benchmarking:

Chrono Tracked Vehicle Simulation Results Summary

Radu Serban, Michael Taylor, Daniel Melanz, Dan Negrut

Simulation Based Engineering Lab

University of Wisconsin – Madison

August 15, 2016

Contents

1 Brief Overview of Chrono 2

2 M113 Model Overview and Assumptions 2

3 Deformable Terrain Model 3

4 Simulation Results 34.1 Steering Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.1.1 Wall to wall turning radius . . . . . . . . . . . . . . . . . . . . . . . . 34.1.2 Steady state cornering . . . . . . . . . . . . . . . . . . . . . . . . . . 44.1.3 Double lane change paved . . . . . . . . . . . . . . . . . . . . . . . . 74.1.4 Double lane change gravel . . . . . . . . . . . . . . . . . . . . . . . . 8

4.2 Side slope stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.2.1 Paved conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.2.2 Deformable terrain conditions . . . . . . . . . . . . . . . . . . . . . . 10

4.3 Grade climbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.3.1 Steerable limiting slope . . . . . . . . . . . . . . . . . . . . . . . . . . 124.3.2 Speed on slope – paved conditions . . . . . . . . . . . . . . . . . . . . 134.3.3 Speed on slope – deformable terrain conditions . . . . . . . . . . . . . 14

4.4 Ride quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.4.1 Random terrain ride limiting speeds . . . . . . . . . . . . . . . . . . . 154.4.2 Half round obstacle ride limiting speeds . . . . . . . . . . . . . . . . . 16

4.5 Obstacle Crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.5.1 Step climb height limit . . . . . . . . . . . . . . . . . . . . . . . . . . 174.5.2 Gap crossing limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.5.3 Trapezoidal fixed barrier limits . . . . . . . . . . . . . . . . . . . . . 194.5.4 Trapezoidal ditch crossing limits . . . . . . . . . . . . . . . . . . . . . 20

4.6 Off road trafficability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.6.1 Single pass soil strength . . . . . . . . . . . . . . . . . . . . . . . . . 214.6.2 Multi pass soil strength limit . . . . . . . . . . . . . . . . . . . . . . 214.6.3 Drawbar pull vs slip performance curve . . . . . . . . . . . . . . . . . 224.6.4 Motion resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.7 Fuel Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.7.1 On-road conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.7.2 Off-road conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

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1 Brief Overview of Chrono

Chrono [2] is an open source multi-physics engine whose development is led by teams atthe University of Wisconsin – Madison and the University of Parma, Italy. It supportsthe simulation of systems of rigid bodies, flexible bodies, and fluids interacting throughtraditional multi-body constraints, friction, and contact. To lower the learning curve fornew users, several toolkits are currently under development or have already been developed.The most relevant of these is Chrono::Vehicle which supports the simulation of both wheeledand track vehicles through a template interface.

2 M113 Model Overview and Assumptions

The Chrono::Vehicle module provides a model of an M113 vehicle as a demonstration instan-tiation of its tracked vehicle templates. This model was modified to bring it in alignmentwith the data provided by the NATO RTG along with engineering approximations to fill inthe remaining required parameters. The track shoes were modeled as geometric primitives(cylinders and rectangular prisms) and were connected together by revolute joints. AlthoughChrono supports the ability to use triangular contact meshes, this higher level of fidelity wasnot used for these benchmarking simulations due to the fidelity of assumptions made in theprovided benchmarking data and benchmarking effort’s focus on rigid terrain. The sprocketprofile was setup as a 2D contact profile whose geometry was based on the M113 demon-stration model. Based on the track assembly algorithm developed for the Chrono::VehicleTracked Vehicle Toolkit, the idler was not fixed in place, but was put on a carrier with aTSDA and a translational joint, acting as a hydraulic tensioner, to preload the track. Thistrack tension method is consistent with the information we found on the M113 in publicdomain (http://www.army-guide.com/eng/product1424.html).

The missing mass properties for the M113 model were generated based on rough engi-neering approximations. For example, the inertia for the vehicle’s chassis was generated byassuming a hollow rectangular prism with 1.75 in thick walls, the largest armor thicknessstated in the provided documents, and the calculated mass of the chassis. The drive sprocketmass and inertia was calculated by assuming a solid cylinder with the provided radius of0.214 m and width of 0.236 m (9.3 in) with a density a quarter of that of steel to accountfor the voids in the actual sprocket design. The idler’s mass properties were generated ina similar manner, except two spaced solid cylinders were used. The road wheel mass wascalculated by solving for the remaining unsprung mass and the inertia was calculated assum-ing two solid spaced cylinders with this combined mass. Assumptions were made for otherparameters, but they are not listed here for brevity. They can be provided upon request.

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3 Deformable Terrain Model

While Chrono provides full support for Discrete Element Method (DEM) granular dynamicsand coupled vehicle – granular terrain simulations, due to time and resource limitations, forthe purpose of these tests we opted to use a more expeditious model for deformable terrain,based on the Soil Contact Model (SCM) [1]. The Chrono implementation provides severalextensions to the original SCM; e.g. non-uniform and adaptive griding and ability to loadterrain profiles from height field or mesh data.

4 Simulation Results

4.1 Steering Performance

4.1.1 Wall to wall turning radius

Wall to wall turn radius (Neutral axis spin maneuver): slow speed, maximum steer input(drive right reverse and left tracks in forward direction to achieve a clockwise vehicle spin),compute the maximum diameter of a plan view trace of vehicle chassis outer most pointsthat will impinge upon a wall of any height and thus prevent the turn maneuver, spinningat least a 360 degrees. Repeat in the counterclockwise direction.

Figure 1: Event 1a: Clockwise wall to wall turning radius.

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Figure 2: Event 1a: Counterclockwise wall to wall turning radius.

4.1.2 Steady state cornering

Steady state cornering: Per SAE J266, asphalt skid pad (friction coefficient = 0.8), 100 feetturn radius, starting at 5 mph increase velocity at constant acceleration rate to achieve ap-proximate expected max speed in 100 seconds. Continue acceleration until loss of traction orunable to maintain turn radius. Plot turn angle and vehicle roll angle vs lateral acceleration.Repeat to get both right and left turns.

Note: For this maneuver, the vehicle was power limited and did not slide out of the turn.The steering required at the peak speed was greater than 0.5, meaning that a reverse torquewas applied to the inside track.

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Figure 3: Event 1b: Steady state cornering (counterclockwise). Speed vs. time.

Figure 4: Event 1b: Steady state cornering (counterclockwise). Vehicle path.

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Figure 5: Event 1b: Steady state cornering (counterclockwise). Kinematic turn ratio.

Figure 6: Event 1b: Steady state cornering (clockwise). Speed vs. time.

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Figure 7: Event 1b: Steady state cornering (clockwise). Vehicle path.

Figure 8: Event 1b: Steady state cornering (clockwise). Kinematic turn ratio.

4.1.3 Double lane change paved

Double lane change paved: Determine max attainable speed per AVTP 03-160W, hard sur-face, mu= 0.8

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Note: For this maneuver, the vehicle was power limited. The steering required was greaterthan 0.5, meaning that opposite torques were applied to each track.

Figure 9: Event 1c: Animation snapshot for a double lane change maneuver.

Figure 10: Event 1c: Double lane change maneuver on paved road.

4.1.4 Double lane change gravel

Double lane change gravel: Determine max attainable speed per AVTP 03-160W, hard sur-face, mu=0.5

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Note: For this maneuver, the vehicle was power limited. The steering required was greaterthan 0.5, meaning that opposite torques were applied to each track.

Figure 11: Event 1d: Double lane change maneuver on gravel.

4.2 Side slope stability

4.2.1 Paved conditions

Paved (mu=0.8) surface serpentine steerable slope speed limit: Determine maximum 30%side slope speed maneuverable. This is defined as the maximum speed on a 30% side slopefor which the vehicle can traverse across a 30% side slope, first in a straight path line for20 meters, then execute a downhill obstacle avoidance maneuver in less than 30 meters oftraverse path length, around a 3 meter wide obstacle while recovering to the original straightline path and elevation on the slope.

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-20 -15 -10 -5 0 5 10 15 20x-position (m)

0

1

2

3

4

5

6

7

8

9

10

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 2a - Side slope stability

Speed = 4 m/s4.5 m/s5 m/s5.5 m/s6 m/s

Figure 12: Event 2a: Vehicle position for side slope stability (paved conditions).

Conclusion: 5 m/s is the maximum speed.

4.2.2 Deformable terrain conditions

Deformable terrain serpentine steerable 20% slope speed limit. Determine maximum maxi-mum speed for obstacle avoidance (per 2a description) on a 20% side slope on sand definedby the LETE sand in Ref 3 (Wong, Garber, and Preston-Thomas, 1984).

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Figure 13: Event 1c: Animation snapshot for side slope obstacle avoidance simulation (vehiclespeed: 4 m/s).

-20 -15 -10 -5 0 5 10 15 20x-position (m)

-1

0

1

2

3

4

5

6

7

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 2b - Side slope stability

Speed = 1 m/s2 m/s3 m/s4 m/s5 m/s

Figure 14: Event 2b: Vehicle position for side slope stability (deformable conditions).

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Conclusion: 4 m/s is the maximum speed.

4.3 Grade climbing

4.3.1 Steerable limiting slope

Max steerable/brake-able up slope and down slope. For paved (mu=0.8) surface determinemax up slope and down slopes for which a 3 meter wide obstacle avoidance maneuver canbe executed in 30 meter s of path length while recovering original path line.

-30 -20 -10 0 10 20 30x-position (m)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3a - Grade Climbing

Slope = 60%65%70%75%80%85%

(a)

0 5 10 15 20 25 30 35Time (s)

0

1

2

3

4

5

6

7

8

Veh

icle

Spe

ed (

m/s

)

Chrono::Vehicle M113 - Event 3a - Grade Climbing

Slope = 60%65%70%75%80%85%

(b)

Figure 15: Event 3a: Vehicle position for upward grade climbing for paved conditions.

Conclusion: Maximum slope is 75% at approximately 1 m/s.

-30 -20 -10 0 10 20 30x-position (m)

-1

0

1

2

3

4

5

6

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3a - Grade Climbing

Slope = -30%-40%-50%-55%-60%-65%

(a)

-30 -20 -10 0 10 20 30x-position (m)

-2

0

2

4

6

8

10

12

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3a - Grade Climbing

Slope = -20%-30%-40%-50%-55%-60%

(b)

Figure 16: Event 3a: Vehicle position for downward grade climbing at 2 m/s (left) and 3m/s (right) for paved conditions.

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-30 -20 -10 0 10 20 30x-position (m)

-5

0

5

10

15

20

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3a - Grade Climbing

Slope = 0%-5%-10%-15%-20%-30%-40%

(a)

-30 -20 -10 0 10 20 30x-position (m)

-10

-5

0

5

10

15

20

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3a - Grade Climbing

Slope = 0%-5%-10%-15%-20%-30%-40%

(b)

Figure 17: Event 3a: Vehicle position for downward grade climbing at 4 m/s (left) and 5m/s (right) for paved conditions.

Conclusion: Max slope for 2 m/s: -60%; Max slope for 3 m/s: -50%; Max slope for 4m/s: -30%; Max slope for 5 m/s: -5%

4.3.2 Speed on slope – paved conditions

Speeds on grades. Determine maximum speed on grades up to maximum steerable up slope.

Figure 18: Event 3b: Vehicle top speed for grade climbing (paved conditions).

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4.3.3 Speed on slope – deformable terrain conditions

Deformable terrain grade limits and speeds (initial benchmark on dry sand). For LETE sandfrom Ref 3 (Wong, Garber, and Preston-Thomas, 1984) determine maximum steerable upslope and down slopes and maximum speed on grades up to the maximum up slope.

-30 -20 -10 0 10 20 30x-position (m)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3b - Grade Climbing

Slope = 35%40%45%50%55%60%65%

(a)

0 5 10 15 20 25 30 35Time (s)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Veh

icle

Spe

ed (

m/s

)

Chrono::Vehicle M113 - Event 3b - Grade Climbing

Slope = 35%40%45%50%55%60%65%

(b)

Figure 19: Event 3b: Vehicle position for upward grade climbing for deformable terrain.

Conclusion: Maximum slope is 55% at approximately 1.75 m/s.

-30 -20 -10 0 10 20 30x-position (m)

-1

0

1

2

3

4

5

6

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3b - Grade Climbing

Slope = -25%-30%-35%-40%-45%-50%

(a)

-30 -20 -10 0 10 20 30x-position (m)

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3b - Grade Climbing

Slope = -25%-30%-35%-40%-45%-50%

(b)

Figure 20: Event 3b: Vehicle position for downward grade climbing at 2 m/s (left) and 3m/s (right) for deformable terrain.

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-30 -20 -10 0 10 20 30x-position (m)

-4

-3

-2

-1

0

1

2

3

4

5

6

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3b - Grade Climbing

Slope = 0%-5%-10%-15%-20%-25%

(a)

-30 -20 -10 0 10 20 30x-position (m)

-2

0

2

4

6

8

10

12

14

16

18

y-po

sitio

n (m

)

Chrono::Vehicle M113 - Event 3b - Grade Climbing

Slope = 0%-5%-10%-15%-20%-25%

(b)

Figure 21: Event 3b: Vehicle position for downward grade climbing at 4 m/s (left) and 5m/s (right) for deformable terrain.

Conclusion: Max slope for 2 m/s: -45%; Max slope for 3 m/s: -45%; Max slope for 4m/s: -10%; Max slope for 5 m/s: -5%

4.4 Ride quality

4.4.1 Random terrain ride limiting speeds

Random terrain ride limiting speeds: Determine 6 watt ride limiting speeds due to verticaldriver accelerations on standard 2D profiles provided.

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Figure 22: Event 4a: Example absorbed power simulation run (Single speed).

Figure 23: Event 4a: Random terrain ride limiting speeds for each profile.

4.4.2 Half round obstacle ride limiting speeds

Half round obstacle ride limiting speeds: Determine 2.5G ride limiting speeds due to verticaldriver accelerations on standard half round profiles from 4 inches to 12 inches.

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Figure 24: Event 4b: Animation snapshot for a 4 inch obstacle crossing simulation.

Figure 25: Event 4b: Half-round obstacle. Ride limiting speeds.

4.5 Obstacle Crossing

4.5.1 Step climb height limit

Step climb height limit: determine maximum traversable height in forward direction.

Note: For this maneuver, the vehicle was able to climb over a maximum vertical wall of

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30 inches. Due to the powertrain assumptions and the contact model used for the track,after a couple of attempts the track would catch the top of the step and would pull thevehicle over the vertical wall.

Figure 26: Event 5a: Animation snapshot for a max step climb simulation.

Figure 27: Event 5a: Step climb height limit; maximum step height: 30 inches

4.5.2 Gap crossing limits

Gap crossing limits: determine maximum gap traversable in forward direction.

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Note: For this maneuver, the vehicle started from a stop shortly before the gap and thenaccelerated with full throttle. The maximum gap was determined to the nearest 5 inch tobe 125 inches.

Figure 28: Event 5b: Gap crossing limit; maximum gap width: 125 inches

4.5.3 Trapezoidal fixed barrier limits

Trapezoidal fixed barrier limits: determine traversability limits for obstacles parameterizedby trapezoidal slope angle, barrier height, and barrier top surface width. Assume 12 differ-ent obstacles generated by the combinations resulting from the following obstacle parametervalues: height (30 inches), top/bottom widths :6”, 30”, 140”; up angles: 16 deg, 26 deg, 38deg, 68 deg.

Note: The vehicle was able to climb all of the specified trapezoidal barriers.

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Figure 29: Event 5c: Trapezoidal fixed barrier; Vehicle CG Position for the 6” wide, 16◦ barrier

Figure 30: Event 5c: Trapezoidal fixed barrier; Vehicle CG Position for the 140” wide, 68◦ barrier

4.5.4 Trapezoidal ditch crossing limits

Trapezoidal ditch crossing limits: determine traversability limits parameterized by trape-zoidal slope angle, ditch depth, and ditch bottom surface width. Assume 12 different ditch

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obstacles generated by the combinations resulting from the following obstacle parameter val-ues: depth (30 inches), top/bottom widths : 6”, 30”, 140”; down angles (for ditch obstacles):16 deg, 26 deg, 38 deg, 68 deg.

Note: The vehicle was able to traverse all of the specified trapezoidal ditches.

Figure 31: Event 5d: Trapezoidal Ditch Crossing; Vehicle CG Position for the 140” wide, 68◦ ditch

4.6 Off road trafficability

4.6.1 Single pass soil strength

Single pass soil strength limit. Determine maximum gross vehicle weight traversable in onepass including reversing back through the path per standard VCI measurement methods.

4.6.2 Multi pass soil strength limit

Multi pass soil strength limit. Determine max GVW traversable for 50 passes (forward andreverse).

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0 5 10 15 20 25Weight (kN)

6

6.5

7

7.5

8

8.5

9

Tim

e/pa

ss (

s)

Chrono::Vehicle M113 - Event 6 - Multi-Pass

(a)

0 5 10 15 20 25Weight (kN)

4

4.2

4.4

4.6

4.8

5

5.2

5.4

5.6

Spe

ed/p

ass

(m/s

)

Chrono::Vehicle M113 - Event 6 - Multi-Pass

(b)

Figure 32: Event 6a: Average time (left) and speed (right) per pass for 10 passes as afunction of vehicle weight.

Note: In an effort to speed up computation times, 10 passes were used instead of 50 and thetime per pass was recorded.

4.6.3 Drawbar pull vs slip performance curve

Drawbar pull vs slip performance curve. For the LETE sand and standard M113 GVW,determine the drawbar pull at 2 mph and at stall, assuming drawbar attached at rear hitchlocation. See Ref 3 (Wong, Garber, and Preston-Thomas, 1984).

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-1.5 -1 -0.5 0 0.5 1Slip [-]

-30

-20

-10

0

10

20

30

40

Dra

wba

r P

ull [

kN]

Figure 33: Event 6c: Drawbar pull vs slip performance curve.

4.6.4 Motion resistance

Motion resistance (MR) (powered , towed). Determine powered and towed motion resistancecoefficients in LETE sand. Powered motion resistance is defined to be MR at zero drawbarpull.

4.7 Fuel Economy

4.7.1 On-road conditions

On-road. For a given 3D path loop determine net terrain dependent motion resistance coef-ficient.

Note: The vehicle was given a target speed of 7m/s. This required the vehicle to brakedownhill in order to maintain this speed. Uphill, the vehicle was power limited and could

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not maintain the target speed of 7m/s. The final value for the Motion Resistance Coefficientwas 0.1082.

Figure 34: Event 7a: Vehicle CG Position vs. Vehicle Speed.

Figure 35: Event 7a: Vehicle CG Position vs. Powertrain Power.

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Figure 36: Event 7a: Vehicle CG Position vs. Energy Used by the Powertrain.

Figure 37: Event 7a: Distance Traveled vs. Motion Resistance Coefficient (Cumulative En-ergy/(Cumulative Distance x GVW)).

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4.7.2 Off-road conditions

Off-road deformable terrain. For a given 3D path loop of LETE sand determine net terraininduced motion resistance coefficient.

While Chrono is capable of performing this test on deformable terrain, we were unable to doso due to time and resource limitations. As an example of what the results might look like,a comparison between the motion resistance coefficient for rigid and LETE sand deformableterrain was generated for the first 500m of the Fuel Economy path.

Figure 38: Event 7b: Distance Traveled vs. Motion Resistance Coefficient (Cumulative En-ergy/(Cumulative Distance x GVW)) for the first 500m.

Acknowledgments

The development of Chrono has been supported with funding from the following projects:

• U.S. Army Research Office RIF W56HZV-14-C-0254 ”A Physics-based High Perfor-mance Computing Capability for Ground Vehicle Mobility Analysis”

• U.S. Army TARDEC, CREATE-GV project, W56HZV-08-C-0236 ”Development of aHigh Performance Computing Software Infrastructure for the Modeling and Simulationof Multibody Dynamics Applications: Part 1” (wheeled vehicles)

• U.S. Army TARDEC, CREATE-GV project, W56HZV-08-C-0236 ”Development of aHigh Performance Computing Software Infrastructure for the Modeling and Simulationof Multibody Dynamics Applications: Part 2” (tracked vehicles)

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• U.S. Army Research Office, W911NF-15-1-0386 ”An Instrumentation Request for Up-grading a Mid-size Heterogeneous Computing System Supporting Research and Edu-cational Activities in Computational Dynamics”

• U.S. Army Research Office, Math Division, W911NF-12-1-0395 ”A Homogenization-Driven Multiscale Approach for Characterizing the Dynamics of Granular Media andits Implementation on Massively Parallel Heterogeneous Hardware Architectures”

References

[1] Rainer Krenn and Andreas Gibbesch. Soft soil contact modeling technique for multi-body system simulation. In Trends in computational contact mechanics, pages 135–155.Springer, 2011.

[2] A. Tasora, R. Serban, H. Mazhar, A. Pazouki, D. Melanz, J. Fleischmann, M. Taylor,H. Sugiyama, and D. Negrut. Chrono: An open source multi-physics dynamics engine. InT. Kozubek, editor, High Performance Computing in Science and Engineering – LectureNotes in Computer Science, pages 19–49. Springer, 2016.

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