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Development of a mathematical model for evaluatingchild occupant behaviour in the case of a vehicleside impact simulationM-D Surcel & M Goua École Polytechnique de Montreal – Mechanical Engineering Department, Box 6079,Station CV, Montréal (Québec), Canada, H3C 3A7b École Polytechnique de Montreal – Mechanical Engineering Department, Box 6079,Station CV, Montréal (Québec), Canada, H3C 3A7Published online: 08 Jul 2010.

To cite this article: M-D Surcel & M Gou (2005) Development of a mathematical model for evaluating child occupantbehaviour in the case of a vehicle side impact simulation, International Journal of Crashworthiness, 10:1, 111-118, DOI:10.1533/ijcr.2005.0330

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© Woodhead Publishing Ltd 0330 111 IJCrash 2005 Vol. 10 No. 1 pp. 111–118

Corresponding Author:Professor Michel GouEcole Polytechnique de Montréal, PO Box 6079, Station ‘Centre-ville’Montréal, Québec, Canada, H3C 3A7Tel: +1 (514) 340-4669 Fax: +1 (514) 340-5867Email: michel.gou@polymtl.ca

INTRODUCTION

Child passenger safety is a major concern for regulatoryorganisation as well as for child restraint systems andvehicle manufacturers. Statistics show that road collisionsare the primary cause for the death and the injury ofchildren, despite continuous improvements incrashworthiness and child restraint system effectiveness.Child restraint systems offer a specialized protection forthe child occupant, whose body structure is still immatureand growing. Using the child restraint system, the childis linked to the vehicle structure and participates to theimpact in the same time as the structure. The tight link tothe car structure solves only part of the problem because,in order to optimize the body impact tolerance, theremaining load should be distributed as widely as possibleon the strongest region of the child body.

Moreover, the effectiveness of child restraint systemshas been well demonstrated for frontal impact but theperformances of these protective devices in side-impactsituation were not, as yet, clearly demonstrated. Applicableregulations are only stipulating that the child passengershould not be ejected from the car in a side impact howevercrash data shows that there are side impact situations wherethe child restraint system does not offer sufficientprotection, resulting in serious injuries or even the deathof the child occupant.

Therefore all the aspects concerning the requirementsand the test procedures for the child passenger side impactprotection are presently under discussions: test type (sledor vehicle body), acceleration pulse, child dummy,instrumentation and even the child restraint systemeffectiveness assessment criteria.

Reliable and realistic procedures are necessary to decideabout these major issues and many related problems andin this context numerical modelling is a relativelyinexpensive and efficient tool that could be used to evaluatethe performance of child restraint systems.

Thus this project was aimed at the development of anumerical method to simulate the behaviour of a child

Development of a mathematical model forevaluating child occupant behaviour in thecase of a vehicle side impact simulation

M-D Surcel* and M Gou***École Polytechnique de Montreal – Mechanical Engineering Department, Box 6079, Station CV, Montréal(Québec), Canada, H3C 3A7, E-Mail: marius-dorin.surcel@sympatico.ca**École Polytechnique de Montreal – Mechanical Engineering Department, Box 6079, Station CV, Montréal(Québec), Canada, H3C 3A7 E-Mail: michel.gou@polymtl.ca

Abstract: The effectiveness of child restraint systems has been well proven for frontal collisions butthe performances of the protective devices in side-impact situations were not, as yet, clearly demonstrated.

This research programme was aimed at the development of a numerical method to simulate thebehaviour of a child passenger, restrained in a protective device, in the case of a vehicle side impact.

The MADYMO software was chosen to build the model using finite element and multi-bodymethods. The side wings of the child restraint system and the vehicle body have been modelled by thefinite-element technique, to allow for a better representation of the contacts and to allow the simulationof the vehicle body deformation.

The model has been evaluated against similar test data. The simulation results were generally veryclose to the experimental data but differences could be observed for some injury criteria, mainly dueto a different initial position of the child dummy. The model exploitation aims to assess differentinstallation configurations, dummy model influence and consequences of vehicle intrusion.

Key words: Child restraint system, ISOFIX, MADYMO, side impact, simulation.

doi:10.1533/ijcr.2005.0330

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passenger restrained in a protective device in the case ofa vehicle side impact.

METHODOLOGY

Child restraint system and vehicle body models have beenbuilt using finite element and multi-body techniques. TheMADYMO software was chosen to build the model becauseit reduces the computational time and the related costs,allows the use of already validated dummy models fromthe MADYMO library and makes possible the comparisonwith other simulations created with the same software. Toreduce the costs and analysis time, the model was mainlybased on a multi-body method. However the side wingsof the child restraint system and the vehicle body havebeen modelled by the finite-element technique, to allowfor a better representation of the contacts between thechild dummy and the restraining device and the structureof the vehicle and to make possible the simulation of thevehicle body deformation.

The reverse engineering method was mainly used toobtain the necessary constructive data, because themanufacturer information is generally consideredconfidential and not easily accessible.

The second step was to validate the model against similartest data. Table 1 presents the parameters of the modelsand simulation.

both femurs; between each femur and the abdomen, thethorax, the neck and the head; between both tibias; betweeneach tibia and the neck and the head; between both arms;between each arm and the neck and the head. The modelused has been validated by TNO for frontal loading.

A special program has been elaborated to position thechild dummy in the child restraint system by applyingthe gravitational force on the child dummy, which allowsfor an equilibrium state in order to avoid the initialaccelerations that could be caused by the joints stiffness.

CHILD RESTRAINT SYSTEM MODEL

For the chosen child dummy model, the required childseat is the convertible restraint system designed for useby infants and toddlers. The Cosco Touriva child seat waschosen, because both test results and a specimen wereavailable for analysis.

A shell and a support that comes in contact with thevehicle bench cushion compose the child restraint system.The shell is mounted on the support, more or less rigid,depending on the desired seat functionality. The inside ofthe shell is covered with a padding that satisfies energyabsorption requirements. The seat is equipped also withan inclination adjustment button, a rear support and aharness.

The shell is made from polypropylene, vitreous atambient temperature. Moreover, the polymer behaviouris very complex; the same material might differently reactat the same solicitation and it is very sensitive with thetemperature, hydrostatic pressure and deformation speed.It might behave as a rubber, at high temperatures, or as abrittle material at low temperatures. Various laws, the linear-elastic law, the Johnson-Cook elasto-plastic model or theelasto-viscoplastic model of Boyce, Parks and Argon, canbe used to describe the behaviour of this material butnone is really satisfactory. To characterize this material,the elasto-plastic isotropic model was chosen, being theavailable MADYMO model with the closest behaviour tothe properties described by Lefeuve, Verron, Peseux,Delcroix and Rabeony [3].

The central region of the child seat has been builtusing sixty-eight very thin ellipsoids with nearly rectangularcross-sections and four cylinders. The child seat side wingshave been reconstructed using finite elements, to allowfor a better representation of the contacts between thechild dummy and the restraining device and between theside wings of the child restraint system and the vehicleinterior. Because MADYMO software has no meshingtools, the coordinates for each node must be inputted foreach element. For this reason the mesh has to be obtainedfrom other software and CATIA has been chosen for thispurpose. Coordinates of arbitrary points were measuredusing the OPTOTRAK - POLARIS equipment(optoelectronic digitizer with LED pointer). The wingshave been reconstructed using this cloud of points andmeshed with CATIA software and the nodes and the

Table 1 Parameters of the models and simulation

System Input data

Vehicle body – Dimensional characteristics– Material properties– Position and dimensions of anchorages– Safety belts mechanical characteristics– Vehicle body deformation in case of side

impactChild – Dimensional characteristicsRestraint – Material propertiesSystem – Harness mechanical characteristics

– Acceleration pulseChild dummy – According to MADYMO library model

– Acceleration pulse

CHILD DUMMY MODEL

A majority of tests and studies have been done using threeyears old dummies and test results are readily availablefor the Hybrid III three years old child dummy. For thesereasons the Hybrid III three years old child dummy waschosen for the simulation.

The Hybrid III – 3 years old child dummy numericalmodel is available in the MADYMO Data Base [1]. Themodel consists of 28 ellipsoids while some head regionsare built using the finite elements method. The contactbetween head and thorax is defined by default andadditional contacts were defined for our model: between

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elements were inputted in the MADYMO programme(Figure 1) which was used to assemble together (Figure2) the multi-body central part and the finite elements sidewings.

Vehicle body dimensional characteristics andconstitutive material properties were either measured orexperimentally determined on a similar vehicle and itscomponents. The vehicle safety belt characteristics werealso either measured or adapted from available literaturedata [2]. The vehicle body structure is illustrated in Figure4.

Cloud CATIA surface CATIA mesh MADYMO mesh

Figure 1 Child restraint system side wings digitization.

The inertial properties of the complete child restraintsystem were computed by MADYMO, based of those ofthe side wings and of the central part of the seat. A specialprogram was elaborated to compute the inertial propertiesof the central part. For the finite element parts, MADYMOcalculated the inertial properties using the dimensionalcharacteristics and the material properties. A contactstiffness function was also defined for the padding of thechild restraint system.

The harness straps were represented using MADYMObelt segments. The release button and the harness retainerclip were built by ellipsoids and the harness characteristicswere measured or adapted from the available literaturedata [2]. The installation of the harness on the child dummyis presented in Figure 3.

VEHICLE MODEL

Since readily available test results (vehicle side impacttest and child restraint system test) had been performedon a Pontiac Grand Am 1999, this vehicle model waschosen for the simulation.

(a) COSCO Touriva child seat [4] (b) MADYMO model

Figure 2 Child restraint system model.

Figure 3 Child restraint system harness installation.

Figure 4 Vehicle body structure (adapted from [5]).

The rear bench and the front seats were representedusing ellipsoids and they were linked to the referencespace using point restraints (a combination of threemutually perpendicular parallel springs and dampers), inorder to allow for their displacement in the case of theside impact. The contact stiffness for the rear bench cushionand rear bench back was defined by force-deflection curves(Table 2).

Vehicle side frame, rear doors, rear panel, rear shelf,rear glass and rear doors glasses were built using finiteelements, to allow for a better representation of the contactsbetween the vehicle interior and child dummy and childrestraint system side wings and to make possible thesimulation of the vehicle body deformation, based onavailable test data. Arbitrary points were picked to digitizethe interior panels of the rear door (using theVISUALEYEZ equipment, electronic digitizer with laserpointer) and the metallic parts of the rear door (using theOPTOTRAK – POLARIS equipment). The rear door

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components were reconstructed using these clouds ofpoints and meshed with CATIA software. The nodes andelements were inputted in MADYMO programme withinwhich the door was assembled (Figures 5 and 6).

belt installation was also chosen because readily availabletest results were obtained with the child restraint systemmounted in this configuration. A supplementary top tethercan also be used (Figure 8).

Table 2 Contact stiffness for the rear bench cushion and rear bench back

Friction coefficient 0, 3Damping coefficient 200

Loading

Force, N 0 500 800 1150 2150 5250Deflection, m 0 0,030 0,075 0,105 0,135 0,165

Unloading

Force, N 0 580 1100 – – –Deflection, m 0 0,087 0,150 – – –

Cloud CATIA surface CATIA mesh MADYMO mesh

CATIA surfaces MADYMO mesh

Figure 5 Rear door interior panel digitization.

Figure 6 Digitization of the metallic parts of the rear door.

The side frames of the vehicle body and the roof weremodelled based on the measurements and analysisperformed on a similar vehicle body.

The mesh dimension for different components andregions was chosen considering both the desired accuracyof the representation and simulation and the limitedpossibilities of the available computational resources. Table3 and Figure 7 present the vehicle model.

CHILD RESTRAINT SYSTEM INSTALLATION

Accident data shows that the most dangerous position inthe vehicle is the near side impact position [6] which wasthus the chosen configuration for our model. Vehicle safety

Table 3 Vehicle model description

Component Description of constitutive elements

Rear bench 4 ellipsoidsLeft seat 3 ellipsoidsRight seat 3 ellipsoidsFloor Finite elements (40 nodes and 27

elements)Left rear door panel Finite elements (537 nodes and 471

elements)Right rear door panel Finite elements (232 nodes and 191

elements)Left rear door Finite elements (1603 nodes and

1412 elements)Right rear door Finite elements (187 nodes and 149

elements)Left body frame Finite elements (423 nodes and 383

elements)Right body frame Finite elements (351 nodes and 317

elements)Body roof Finite elements (33 nodes and 23

elements)Left rear window glass Finite elements (12 nodes and 6

elements)Right rear window glass Finite elements (12 nodes and 6

elements)Rear central glass Finite elements (18 nodes and 10

elements)

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SIMULATION

To simulate the side impact, both a lateral accelerationfield and the gravity field were applied to the child dummyand to the child restraint system.

The lateral acceleration field, which corresponds to animpact speed of 33,8 km/h, with a peak acceleration of 26g (255 m/s2), complies with SNCAP (Side impact – NewCar Assessment Program) specifications and was usedduring the tests performed by NHTSA in 2001 [7] (Figure9). For this test, a Hybrid III 3-year-old dummy waspositioned, in a Cosco Touriva child seat, in the rearoutboard position nearside to the impact of the PontiacGrand Am 1999. The Grand Am sled test buck, previouslyused for frontal testing, was turned 90° to the direction of

the sled motion. An explicit Euler algorithm with a timestep of 2.5 × 10–5 second performs the computation. Thetotal computational time for a 200 ms simulation isapproximately 19 minutes.

The simulation results show that both the child dummyand the child restraint system moved under the action ofthe acceleration field. The vehicle safety belts and thechild restrain harness were tensioned and the child dummyhead entered into contact with the left side wing of thechild restraint system and consequentially with the interiorleft rear door panel. The child dummy was pushed to theright by the reaction forces due to the impact with thedoor panel and by the elastic forces in the harness and inthe seat belt and consequentially the dummy hit the rightside wing of the restraint system and pushed the childseat to the right.

Figure 10 illustrates the model during the simulationof the side impact.

Figure 7 Vehicle model.

(a) Safety belt installation (b) Top tether representation

Figure 8 Child restraint system installation.

Figure 10 Simulation of the side impact.

EVALUATION RESULTS

The simulation results were compared with the results ofthe above-mentioned tests, performed by NHTSA in 2001,[7] and [8], and with the Injury Assessment ReferenceValues (IARV), stipulated by FMVSS 208 and FMVSS213. However these injury criteria are for frontal impactand may not accurately reflect the risk of injury in sideimpact and the corresponding Injury Assessment ReferenceValues should be used for reference purposes only.

Table 4 presents the peak values of some injury criteria.Peak head acceleration was computed based on the availabletest signals [8].

The simulation results come generally close to theexperimental data but differences could be observed forneck compression and neck flexion, possibly due to aslightly different initial position of the child dummy. Childdummy position was not completely described in the actualtest making it difficult to exactly reproduce the testconfiguration.

300

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200

150

100

50

00 0.02 0.04 0.06 0.08 0.1

Acc

eler

atio

n, m

/s2

Time, s

Figure 9 Side impact pulse (adapted from [7]).

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Head injury criteria and thorax acceleration obtainedthrough the simulation are higher than the reference valuesbut thorax deflection and neck forces are less that therelated reference values.

Figures 11 and 12 illustrate the comparisons of thevariation of head acceleration and thorax acceleration.These variations were computed based on the availabletest signals [8].

straps and vehicle safety belts straps because MADYMOstandard belt model has fixed attachments points and cannotreproduce the effects of slip on the dummy model. As aresult, some differences between the tested belt and harnessand the belt and harness model behaviour are possible.The effect is not important for the head acceleration sincethe peak is related here to the contact between the dummyhead and the door panel and the two curves coincide atthis point. However, for the thorax acceleration, the peakis given by the brutal stop of chest movement caused bythe restraint forces in the harness and in the belts andthus details of belt and harness model is very important.For this reason, one of the intended improvements to thismodel is the complete modelling of the belts and harnessusing finite element method that will allow for a betterrepresentation of the harness slip across the dummy modeland realistic reproductions of the related contacts.

CONCLUSIONS

This project was aimed at the development of a numericalmethod to simulate the behaviour of a child passengerrestrained in a protective device while involved in a vehicleside impact. Child restraint system and vehicle body modelwere built using multi-body technique together with thefinite element method, to allow for a better representationof the contacts between the child dummy and therestraining device and the structure of the vehicle and tomake possible the simulation of the vehicle bodydeformation.

The model was evaluated for side impact against similartest data. The simulation results were generally very closeto experimental data but differences could be observed forsome injury criteria, probably caused by a slightly differentchild dummy initial position or some differences betweenreal tested belt and belt model characteristics or both.

Although the results of the project successfullyresponded to the initial objectives, the model is offeringmany possibilities of improvement, development andexploitation.

The model can be improved by the refining andexperimental validation of the input data, modelling ofthe belts, the harness and the child dummy using thefinite element method or refining and diversifying thechild restraint system and vehicle models (building a modelslibrary). The first developments will be aimed at evaluatingvarious installation configurations, different child dummiesresponses and the influence of the intrusion against thechild dummy behaviour in the case of side impact.

The simulation can be developed by diversifying theacceleration pulses, simulating the side impact with a barrieror other vehicle in different configurations, studying theinfluence of child restraint system and vehicle parameters(position and distance between anchorages, slack or tensionin the belts and in the harness, misuse of the child restraintsystem etc) and performing accident case studies.

Table 4 Evaluation results

No Injury parameter Simulation Test IARV

1 HIC 15 1001 1085 5702 HIC unlimited 1001 1085 10003 Thorax deflection, mm 6,14 3,56 344 Thorax acceleration –

3 ms, m/s2 639 646 540/5895 Head acceleration, m/s2 1193 1582 –6 Neck tension, N 1251 1143 23407 Neck compression, N 1276 46 21208 Neck extension, Nm 13,8 13,4 –9 Neck flexion, Nm 29,0 10 –

The comparison of head acceleration variation curvesshows good reproduction of the experimental data (Figure11). However the comparison of the thorax accelerationvariation curves shows a time lag between the two peaksand less progressive variation at the beginning, for thesimulation curve (Figure 12). These discrepancies are theresults of using standard MADYMO belt model for harness

1000

800

600

400

200

00 0.1 0.2 0.3

Time, s

Hea

d ac

cele

ratio

n, m

2 /s SimulationTest

Figure 12 Comparison of thorax acceleration variation.

2000

1500

1000

500

00 0.1 0.2 0.3

Time, s

Hea

d ac

cele

ratio

n, m

2 /s

SimulationTest

Figure 11 Comparison of head acceleration variation.

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ACKNOWLEDGEMENTS

This research has been made possible by the fundingsupport of AUTO21 – A Network of Centres of Excellence.

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