Crashworthiness Considerations for Van Structures

118. CAD-FEM Users´ MeetingInternationale FEM-Technologietage

20. - 22. September 2000Graf-Zeppelin-Haus, Friedrichshafen

Crashworthiness Considerations for Van Structures

Frank C. Günther

DaimlerChrysler, Stuttgart, Germany

Summary:

The crash behavior of van structures needs to be analyzed for a wide range of vehicle weights. First, adimensional analysis of van crash problems is presented. Then a simplified model for assessing crashpulses for van structures using Dyna3D is derived. Given a Dyna3D reference solution for thecomplete structure, crash pulses for smaller masses and/or initial velocities can be obtained in verylittle time using a single degree of freedom model.

Keywords:

crash, safety, DYNA3D, automotive

Albert Oswald

3.2.1



1 Introduction: Overview of computational activities for commercial vehicles safetyat DaimlerChrysler

Dyna3D is used for many different problems related to the safety of commercial vehicles. The testsconducted for vans are somewhat similar to those for passenger cars. For heavy trucks, other testsbecome relevant.

1.1 Vans

Dyna3D is used for simulations of:- Euro-NCAP front and side impact (structural/occupant),- Crash pulse for airbag fire/no fire conditions (structural),- Various internal tests (structural/occupant).

1.2 Heavy trucks

Dyna3D is used for simulations of:- ECE R29 cab tests (structural),- Swedish cab tests (structural),- Crash pulse for airbag fire/no fire conditions (structural),- Various internal tests (structural/occupant).

2 Crash pulse of van structures

A crash pulse gives the time history of the rigid-body deceleration of a van structure. It is significantfor occupant safety and the design of restraint systems. Large decelerations should be avoided sincethey make the design of adequate active and passive restraint systems more difficult. Crash pulsesare also used in the fire/no fire conditions of active restraint systems. For a given van structure and agiven type of crash, the crash pulse depends on the characteristic velocity of the crash and thecharacteristic mass.

For stationary crash barriers, the characteristic velocity and characteristic mass are the velocity andmass of the van structure, respectively. For moving barriers, the characteristic velocity is the velocityof the barrier. Assuming ideally inelastic impact, conservation of momentum then gives acharacteristic mass of

,vb

vbc mm

mmm

+=

where bm is the mass of the barrier, and vm is the mass of the vehicle. For crash configurations with

a moving barrier, the characteristic mass is always smaller than the mass of the vehicle and the massof the barrier.

For vans, vm will vary widely for any given structure, since payload constitutes a large percentage of

the maximum vehicle mass. This motivates analyzing the effect of varying vehicle mass on the crashpulse.

3 Dimensional analysis of van crash problems

Dimensional analysis is commonly used in the field of fluid mechanics. However, it can be applied toother physical problems as well.

Let us assume that the global acceleration of a given van structure can be written as a function ofseveral dimensional variables, namely

( ) ( )favgdT fdFvmmtfta ,,,,,; max0= ,

where t is the time, Tm is the total mass of the vehicle, dm is the mass of the deforming part of the

vehicle, 0v is the initial velocity, avgF is the deflection-averaged resultant force on the vehicle

(constand for a given van structure), maxd is the characteristic length of the crush zone (constant for a

given van structure), and ff is the characteristic frequency for filtering the crash pulse.



The dimensional matrix takes on the following form:

Tm dm 0v avgF maxd ff t a

M 1 1 0 1 0 0 0 0L 0 0 1 1 1 0 0 1T 0 0 -1 -2 0 -1 1 -2We need to find 538 =− non-dimensional variables. Let us choose the non-dimensional mass of thecrush zone

1ˆ0,ˆ ≤≤= dT

dd m

m

mm ,

the ratio of energies

1ˆ0,2

1

ˆmax

20

≤≤= EdF

vmE

avg

T

,

the non-dimensional time

max

0ˆd

tvt = ,

the non-dimensional acceleration

20

maxˆv

ada = ,

and the non-dimensional filtering frequency

0

maxˆv

fdf = .

This leads to the reformulated relation

( )

=0

max

max

20

max

0

max

20 ,2

1

,;ˆv

df

dF

vm

m

m

d

tvf

d

vta f

avg

T

T

d .

In other words, the non-dimensional crash pulse (non-dimensional acceleration vs. non-dimensionaltime) only depends on the percentage of mass in the crush zone, the ratio of energies, and the non-dimensional filtering frequency. Fig. 1 shows two Dyna3D runs with the same non-dimensionalvariables. However, the initial velocity for the second run was doubled and the total mass was dividedby four. The plot was made with the time axis of the second run scaled by 0.5 and its accelerationaxis scaled by 4. These factores were obtained from the expressions for dimensionless time anddimensionless acceleration. As expected, the two scaled crash pulses are virtually identical.

In many cases, the effects of variation of the non-dimensional mass of the crush zone and of the non-dimensional filtering frequency can be neglected. This further simplifies the above equation.

4 Simplified model

A simplified model can be obtained by assuming that the van structure consists of a massless, energy-absorbing crush zone and a perfectly rigid rest of the structure, in which the mass of the vehicle isconcentrated. The crush zone has a force/deflection relation for loading

( )dfF = for 0>dd &

with the force F and the displacement d .

This force/deflection relation can be obtained from reference crash pulse that is generated by aDyna3D simulation of the complete structure as follows: From the Dyna3D simulation the globalacceleration time history ( )ta and the global displacement time history ( )td can be extracted. Thenthe equation

( ) ( ) ( )( )tdftamtF c ==



is a parametrized representation of the force/deflection relation.

The simplified model can be written as

( )dfdmc =&& with ( ) 00 =d and the initial velocity ( ) 00 vd =& .

This second-order, non-linear initial value problem can be solved with a smaller mass cm or a smaller

initial velocity 0v , or both. Of course, as shown by the dimensional analysis of the previous section,

there is no fundamental difference between varying initial velocity and varying total mass. Note that alarger mass cm or a larger initial velocity 0v cannot be used, since they would lead to deflections that

are larger than those of the reference solution.

We use Dyna3D with a non-linear spring and a point mass to integrate the above equation. Thescript language Perl is used to extract a load curve from the nodout file of the full structure Dyna3Dreference model and to generate the input deck for the simplified model. CPU time for the simplifiedmodel is on the order of magnitude of a few seconds.

Both filtered and unfiltered acceleration data can be used to obtain the force/deflection curves.Currently, we favor the use of unfiltered acceleration data, since the global displacement and velocityhistory of the reference model can then be reproduced exactly by the simplified model if the originalmass and initial velocity are used.

5 Example structure

To test the quality of the simplified model, an idealized structure shown in Fig. 2 is used. It consists ofa deformable part (left) representing the crush zone and impacting a stonewall, and a rigid part (right)with point masses representing the rest of the vehicle. The crush zone consists of 20% of the totalmass of the structure. Total mass and initial velocity are varied.

Fig. 3 shows the influence of the initial velocity on the crash pulse of the idealized structure, filteredwith a 2000Hz low pass filter. Note that the length of the crash pulse depends on the initial velocity,whereas the magnitude of the acceleration remains about the same. The time axis is dilated.

Fig. 4 shows the influence of the total mass on the crash pulse of the idealized structure. The crashpulse changes in magnitude.

This is the behavior that would be expected by inspection of the differential equation of the simplifiedmodel. Consider now Fig. 5, which shows the effect of different initial velocities on the simplifiedmodel. The crash pulse of a 20kg, 30m/s structure is used as reference solution for theforce/deflection curve. The two other crash pulses are obtained using the simplified model.Comparing Fig. 5 and Fig. 3, we find that the general shape of the crash pulse is reproduced well bythe simplified model. There are, however, noticeable differences especially where the 30m/s crashpulse was used as the reference solution for a 10m/s initial velocity run.

Fig. 6 shows the effect of total mass on the simplified model. The crash pulse of a 60kg, 20m/sstructure is used as reference solution for the force/deflection curve. The 40kg crash pulse from Fig. 4is matched quite well. The 20kg crash pulse is off quite a bit, especially the location of the onset of theplateau.

6 Conclusions

A simplified model for assessing crash pulses for van structures was presented. Given a Dyna3Dreference solution for the complete structure, crash pulses for smaller masses and/or initial velocitiescan be obtained in very little time using a single degree of freedom model. This method seems verypromising where deviations of mass and initial velocity from the reference model are small.



0 1 2 3 4 5 6 7 8 9 10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−0.5

0

0.5

1

1.5

2

2.5

3

−2

0

2

4

6

8

10

12

Time [ms], run 1

Time [ms], run 2

Acc

eler

atio

n [m

m/m

s^2]

, run

1A

cceleration [mm

/ms^2], run 2Dimensional Analysis

run 1run 2

Fig. 1: Demonstration of dimensional analysis.

Fig. 2: Idealized structure with deformable (left) and rigid (right) part.



0 1 2 3 4 5 6 7 8 9 10−2

−1

0

1

2

3

4

5

6

7

8

9

Time [ms]

Acc

eler

atio

n [m

m/m

s^2]

Comparison of Different Initial Velocities

20 kg, 10m/s, 20% def.20kg, 20m/s, 20% def.20kg, 30m/s, 20% def.

Fig. 3: Influence of initial velocity on crash pulse

0 1 2 3 4 5 6 7 8 9 10−1

0

1

2

3

4

5

6

7

8

Time [ms]

Acc

eler

atio

n [m

m/m

s^2]

Comparison of Different Masses

20kg, 20m/s, 20% def.40kg, 20m/s, 20% def.60kg, 20m/s, 20% def.

Fig. 4: Influence of total mass on crash pulse.



0 1 2 3 4 5 6 7 8 9 10−2

−1

0

1

2

3

4

5

6

7

8

9

Time [ms]

Acc

eler

atio

n [m

m/m

s^2]

Comparison of Different Initial Velocity Scalings

20 kg, 10m/s, 20% def.20kg, 20m/s, 20% def.20kg, 30m/s, 20% def.

Fig. 5: Effect of initial velocities on the simplified model.

0 1 2 3 4 5 6 7 8 9 10−1

0

1

2

3

4

5

6

7

8

Time [ms]

Acc

eler

atio

n [m

m/m

s^2]

Comparison of Different Mass Scalings

20kg, 20m/s, 20% def.40kg, 20m/s, 20% def.60kg, 20m/s, 20% def.

Fig. 6: Effect of total mass on the simplified model.

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Crashworthiness Considerations for Van Structures