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The design of a formula student front

impact attenuator

J.M.J. Schormans

MT 10.06

Supervisors:dr. ir. Varvara Kouznetsova

Eindhoven University of TechnologyDepartment of Mechanical EngineeringComputational and Experimental MechanicsSection Mechanics of Materials

Abstract

This research is concerned with the development of a front impact attenua-tor for the University Racing Eindhoven formula student team. Abaqus byDassault Systemes S.A. was used to do finite element calculations in orderto investigate the deceleration properties and deformations of several frontimpact attenuator geometries which are made out of Rohacell foam. Theresults indicate whether or not a foam specimen wil fracture. If a foam speci-men will fracture, the precise location of the fracture and global decelerationinformation can be determined. If a foam specimen does not fracture, decel-eration data and changes in foam geometry can be determined accurately.This research shows that buckling in a foam impact attenuator can be pre-vented and if an anti intrusion plate is used to place the impact attenuatoron, it should be placed vertical. This research recommends the implemen-tation of a damage model to increase the precision of the simulation.

Contents

1 Introduction 3

1.1 University Racing Eindhoven . . . . . . . . . . . . . . . . . . 3

1.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 Design space . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.2 Structure of the report . . . . . . . . . . . . . . . . . . 5

2 The crushable foam material model 6

2.1 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Yield surface . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Flow potential . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Numerical simulations 10

3.1 Uniaxial compression test . . . . . . . . . . . . . . . . . . . . 10

3.2 Simple collision . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.1 The model . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.2 Rohacell 51WF . . . . . . . . . . . . . . . . . . . . . . 12

3.2.3 Rohacell 110IG . . . . . . . . . . . . . . . . . . . . . . 13

3.3 2008/2009 crash test . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.1 Mesh size . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3.2 Yield point prediction . . . . . . . . . . . . . . . . . . 17

4 New design 20

4.1 Design requirements . . . . . . . . . . . . . . . . . . . . . . . 20

4.2 Foam shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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Design of a formula student impact attenuator TU/e

4.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2.2 Anti intrusion plate . . . . . . . . . . . . . . . . . . . 23

5 Conclusion and recommendations 24

5.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2.1 Anti intrusion plate . . . . . . . . . . . . . . . . . . . 24

5.2.2 Foam geometry . . . . . . . . . . . . . . . . . . . . . . 24

5.2.3 Research method . . . . . . . . . . . . . . . . . . . . . 25

5.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.4 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . 25

Department of mechanical engineering 2

Chapter 1

Introduction

1.1 University Racing Eindhoven

University Racing Eindhoven (URE) is a student organized team which hasbeen competing in the Formula Student competition for 5 years. Every yearthey have built a new small single seated car (figure 1.1) and have competedin races in England, Germany and Italy. During these races the car willbe assessed on dynamic and static events. Dynamic events include: accel-eration, skid-pad, autocross and endurance. The static events consist of:design cost and presentation judging, technical and safety scrutineering, atilt, brake and noise test. During the years there has been a lot of techni-cal development within the team and progress is made every year. For the2009/2010 season the team is focusing on two aspects. First, to improvethe previous car and thus fine tuning the design of a new car with a inter-nal combustion engine. Second, the 2008/2009 car will be converted to anelectric powered car.

Figure 1.1: The 2008/2009 URE formula student car

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1.2 Problem description

Part of the safety scrutineering is a Front Impact Attenuator report, inwhich the team has to prove that the car is equipped with a front impactattenuator which is able to reduce the forces of impact keeping in mind thedriver’s safety. The impact attenuator has to comply with rules specifiedby the formula student organization [04]. The most important part of thefront impact attenuator is made out of Rohacell foam. This foam absorbsand dissipates the kinetic energy of the car during a crash. Previous designsof the front impact attenuators made by URE are based on very simple andminimalistic calculations concerning the dimensions of the foam which re-sulted in a ”too soft” crash. The rules specify that the peak deceleration andthe average deceleration must me below 40g and 20g respectively. Previousyears designs have met these specifications with almost half of the valuesrequired. This indicated the design could be optimized with respect to theweight of the design.

This leads to the main goals of this thesis:

• To model the foam material and to make a simulation of the crash testas specified by formula student rules and thus predict its success.

• To minimize material usage in the front impact attenuator and thussaving weight which is a very important factor in motorsport.

• To supply the next generation designers of University Racing Eind-hoven with a reliable method of modeling to make future front impactattenuator designs less time consuming.

• To compare numerical simulations with the impact data gathered dur-ing the 2008/2009 season crash test.



1.2.1 Design space

University Racing Eindhoven’s resources and time are limited. Thereforeit has been chosen to use the mold of the 2008/2009 nose cone again, tomake a carbon shell in which the impact attenuator can be placed. Thismeans the space in which the attenuator can be positioned is limited andpre described. The design space is prescribed by the outside dimensions ofthe carbon shell which can be seen in figure 1.2 and is situated at the frontof the car, in front of the anti intrusion plate (indicated in red). This antiintrusion plate is a 1,5 mm steel plate (or equivalent) which is intended toprevent any objects from reaching the driver’s feet during a crash. Thisplate is situated at the red line and covers the cross section of the car. Thefoam impact attenuator has to be placed inside the carbon shell and on thesteel plate.

Figure 1.2: Design space

1.2.2 Structure of the report

This report is organized as follows. In chapter two, the material modelwhich has been implemented will be explained. Following in chapter three,the model will be calibrated using the experiments performed in the paperof Li et al. [02]. Furthermore, the model will be used to do simulations tocompare a crash test done in 2008/2009 with numerical simulations. Thefourth chapter will deal with the design of the 2009/2010 and designs forthe years after that. Finally chapter five will deal with the conclusions andrecommendations which can be done based on this research.


Chapter 2

The crushable foam materialmodel

This chapter will deal with the crushable foam model which is used to modelthe foam parts of the impact attenuator in Abaqus.

2.1 Elasticity

The model can only be used in combination with a simple linear isotropicelastic material model. In Abaqus the required parameters are the Elasticitymodulus and the Poisson’s ratio.

2.2 Yield surface

The yield surface for the plastic part of the behavior is a von Mises circlein the deviatoric plane and an ellipse in the meridional plane. Within thecrushable foam model there are two different types of hardening possible:volumetric and isotropic hardening. Within the isotropic hardening modelthe yield ellipse is centered at the origin and as it evolves it retains itsoriginal height to width ratio (Fig. 2.1). This model is based on the modelof Deshpande and Fleck [01]. With the volumetric hardening model thepoint on the yield ellipse which represents hydrostatic loading is fixed andthe evolution of the yield surface is driven by the compressive plastic strain(Fig. 2.2). The hardening which occurs under tension is negligible. Theparameters in the figures are explained in table 2.1.

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Figure 2.1: Isotropic hardening in the meridional plane (p,q) [05]

Figure 2.2: Volumetric hardening in the meridional plane (p,q) [05]



Table 2.1: Volumetric model parameters

p = −13 trace σ Pressure stress

q =√

23S : S Mises stress

S = σ + pI Deviatoric stresspc Yield stress in hydrostatic compression

(pc is always positive)

p0 = pc−pt2 Center of the yield ellipse on the p axis

pt Strength of the material inhydrostatic tension

A = pc+pt2 Size of the horizontal axis

B = α A Size of the vertical axis

α = AB Shape factor of the yield ellipse

As this research is concerned with foams with different yield stresses intension and compression and the isotropic hardening model assumes theinitial yield stress in tension and compression are of equal magnitude, thevolumetric model has been chosen. The initial yield surface ellipse is definedby equation (2.1).

F =√q2 + α2(p− p0)2 −B = 0 (2.1)

The yield ellipse develops along the line with slope α, which is constant. Todefine the parameter α there are three material properties required:

• σ0c The initial yield stress in uniaxial compression

• p0c The initial yield stress in hydrostatic compression

• pt The yield strength in hydrostatic tension

Together they are used to calculate α:

α =3k√

(3kt + k)(3 − k)(2.2)

With:

k =σ0cp0c

kt =ptp0c

(2.3)



2.3 Flow potential

The volumetric hardening model uses the following relation to define theplastic strain rate:

εpl = ˙εpl∂G

∂σ(2.4)

With G being the flow potential, chosen to be:

G =

√q2 +

9

2p2 (2.5)

˙εpl is the equivalent plastic strain rate which is defined as:

˙εpl =σ : εpl

G(2.6)

The equivalent plastic strain rate is related to the rate of axial plastic strainin uniaxial compression:

˙εpl =

√2

3εplaxial (2.7)

The shape of this flow potential is depicted in Fig. 2.2

2.4 Hardening

The model assumes that the yield stress in tension remains the same through-out the whole deformation. The yield ellipse intersects the p axis at −pt andpc being the yield stress in tension and compression respectively. Contraryto the yield stress under tension, the yield stress under compression evolvesas a result of compaction (or dilation) of the material. The change in theyield surface can be expressed as a function of the the size of the yield surfaceon the hydrostatic stress axis, pc+pt, as a function of the value of volumetriccompacting plastic strain. With pt constant, this relation is determined byequation (2.8):

pc(εplvol) =

σc(εplaxial)[σc(ε

ptaxial)(

1α2 + 1

9) + pt3 ]

pt +σc(ε

plaxial)

3

(2.8)

in combination with user provided results of an uniaxial compression test,σc(ε

plaxial), along with the fact that εplaxial = εplvol in uniaxial compression for

the volumetric hardening model.


Chapter 3

Numerical simulations

This chapter deals with the calibration of the model on a simple compressiontest performed in the paper of Li et al. [02]. Also in this chapter there willbe a comparison between the numerical simulations and a real live crash testperformed in Januari 2009 at TV Rheinland TNO. The goal of this chapteris to check the material model implementation in Abaqus and to verify themodel against experiments.

3.1 Uniaxial compression test

One of the tests performed in the paper of Li et al. [02] is an uniaxialcompression test of Rohacell-51WF foam. To replicate this test numerically,a quasi static model has been set up using the Abaqus implicit solver. Arectangular block was modeled with a displacement prescribed in such a waythat the final nominal strain would be -75%. An overview of the dimensionsof the foam specimen are given in table 3.1

Table 3.1: Foam specimen dimensions

length of the foam block 200 [mm]height of the foam block 100 [mm]width of the foam block 200 [mm]

In order to fill in the needed hardening data, the results of the uniaxialcompression test from the paper of Li et al. [02] were used. To ensurethe data was suitable for Abaqus, i.e. providing small enough steps forthe iteration process, the hardening curve was fitted with the use of two

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functions. The test was carried out using a single hex element as the stressesand strains are uniform throughout the material for this test. The rest ofthe model parameters are given in table 3.2.

Table 3.2: Material parameters of Rohacell 51WF foam

Density 110 [kg/m3]kt 1.036 [-]k 0.1 [-]Poisson’s ratio 0 [-]Young’s modulus 22 [MPa]Initial yield stress 0.8 [MPa]

A Poisson’s ratio of 0 has been taken in accordance with the research ofFlores-Johnson et al. [03]. Strain rate effects are assumed to be absent inaccordance to the paper of Li et al. [02]. The results of this test can be seenin figure 3.1.

Figure 3.1: Uniaxial compression test on Rohacell 51WF

The results indicate that the model has been properly implemented as thesimulation results match the experimental curve. The material propertiesused in the uniaxial compression test can now be used to model a simplecollision.



3.2 Simple collision

3.2.1 The model

The next step in modeling a crash test is to model a simple collision. Thesimple collision was modeled using a rectangular block of foam material, twoanalytical rigid surfaces and a point mass equivalent to the mass requiredfor the formula student regulatory crash test [04]. One of the analyticalrigid surfaces represents the wall and is fixed in all degrees of freedom. Thesecond analytical surface represents the anti-intrusion plate, which is at thefront of the car. This anti-intrusion plate is fixed in all but the directionperpendicular to the wall. The rectangular foam block is attached to it. Thepoint mass is fixed to the anti intrusion plate which implies it is also fixedin all but the same direction as the anti intrusion plate. The model can beseen in figure 3.2.

Figure 3.2: Abaqus simple collision model

To execute the finite element calculations, Abaqus explicit was used insteadof Abaqus implicit as there are dynamical effects which need to be takeninto account. The prescribed nominal strain has been replaced by a velocityof 7 [ms ] and the point mass was set to be 300 [kg].

3.2.2 Rohacell 51WF

For the simple collision model, the same Rohacell 51WF parameters as forthe uniaxial compression test were used as specified in table 3.2. The de-celeration values and dissipation energy were measured to see if there wereany irregularities that would indicate an error in the model. The results areplotted in figure 3.3.



Figure 3.3: Deceleration (left) and plastic dissipation energy data (right)from the Rohacell 51WF simple collision simulation

The results indicate that there was a constant deceleration, which is inaccordance to the constant frontal area of the foam. At about 4.5 ms, allthe energy is dissipated and the deceleration stops. This indicates that allthe model has been implemented properly.

3.2.3 Rohacell 110IG

Model parameters

As the 2008/2009 impact attenuator was made of Rohacell 110IG foam,a useful model of Rohacell 110IG foam would be required to simulate the2008/2009 collision tests. Both Rohacell 110IG and Rohacell 51WF arepolymethacrylimide foams. As their number indicates, the density of bothfoams is different. For the Rohacell 110IG foam a Young’s modulus of 160MPa and a Poisson’s ratio of 0 were taken. The hardening curve for Ro-hacell 110IG (fig: 3.4) was constructed using the compression strength andthe maximal compression given in the material data sheet provided by themanufacturer [06].



Figure 3.4: The hardening curve for Rohacell 110IG

However this leaves the compression yield stress ratio k (eq. 2.3) and thehydrostatic yield stress ratio kt (eq. 2.3) to be determined. The hydrostaticyield stress ratio is estimated to be 0.1 as indicated in the Abaqus usermanual [05]. However, the compression yield stress ratio is not even ap-proximately known. The simple collision model was used to investigate theinfluence of the compression yield stress ratio on the deceleration and theplastic dissipation energy, the most important parameters for a crash testsimulation. The simulation has been repeated several times using differentvalues for the compression yield stress ratio. The results of the simulationsare depicted in figure 3.5 showing the plastic dissipation energy and decel-eration.

Figure 3.5: Plastic dissipation energy (left) and deceleration (right) at var-ious compression yield stress ratios, other model parametersare given in table: 3.3

As the results indicate there is no difference in energy dissipation and littledifference between the deceleration for the different ratios. It has beenchosen to model the 2008/2009 crash test with a compression yield strengthratio of 1.036 because this was the value calculated using the paper of Li[02] for the Rohacell 51WF foam. The material parameters used to modelRohacall 110IG foam are summarized in table 3.3



Table 3.3: Material parameters of Rohacell 110IG foam

Density 110 [kg/m3]kt 1.036 [-]k 0.1 [-]Poisson’s ratio 0 [-]Young’s modulus 160 [MPa]Initial yield stress 2 [MPa]

To examine the difference between the Rohacell 51WF foam and the Roha-cell 110WF foam. The dimensions of the simple collision test were changedin such a way that the energy of the collisions would be the same for Roha-cell 51WF and for Rohacell 110IG i.e. altering the frontal area of the foamblock and thus the mass of the foam block. The dimensions of the Rohacell110IG block are l ∗ b ∗ h: 0.2 ∗ 0.097 ∗ 0.097 [m]. It was chosen to alter themass by changing the surface and not the length to keep the decelerationdistance the same. The results of the plastic dissipation energy and thedeceleration values are shown in figure 3.6.

Figure 3.6: Comparison between the plastic dissipation energy and decel-eration data of the Rohacell 110IG and Rohacell 51WF colli-sions

As expected, the deceleration of the Rohacell 110IG foam is shorter but ofgreater magnitude. There is a difference in plastic dissipation energy, whichcan be related to the difference in frontal surfaces. The Rohacell 51WFblock’s surface is larger so a larger surface will be able to use the elasticarea in the stress-strain diagram to dissipate energy.



3.3 2008/2009 crash test

In preparation for the races in 2009, two crash tests were carried out. Therewas the URE05 nose cone design, and there was a foam block used. Thisparagraph wil deal with the crash of the foam specimen. The old URE05nose cone consisted out of a carbon fiber shell with four foam pads laminatedin the sides. However, this nose cone has not been modeled because there isa large role of carbon fiber concerning the evolution of the shape of the coneduring the crash and a model of the carbon fiber shell has not been includedin the present work. The foam block was modeled using similar analyticalrigid planes as used in the model of the simple collision. The Abaqus modelfor the crash test and the actual test set up are shown in figure 3.7, thedimensions of the model are listed in appendix A.

Figure 3.7: The real foam specimen test (left) and the Abaqus model(right)

3.3.1 Mesh size

In order to provide accurate predictions, the mesh size of the model is veryimportant. The mesh size has to be small enough to accurately modeldeformation of the material while at the same time, a smaller mesh size willlead to large computation times. For this research, an investigation has beendone to find an ideal mesh size to model the foam specimen. Decelerationgraphs obtained with models with different mesh sizes have been compared.The comparison of these graphs can be seen in figure 3.8.

It can be seen from figure 3.8 that the differences between the graphs de-crease along with the mesh size. The mesh sizes of 0.02 and 0.015 almostdo not differ anymore. Taking this comparison into account along with thefact that simulations with an even smaller mesh size will take more time, amesh size of 0.015 has been taken to model the foam specimen.



Figure 3.8: Deceleration graphs for different mesh sizes

3.3.2 Yield point prediction

Although the model does not include a damage model, the model is stil validup to the point of fracture. The point of the fracture can be indicated in themodel. To determine the point at which the material cracks, a closer lookis taken at the yield surface shown in figure 2.2. The assumption was madethat there is negligible hardening in tension. This implies that equation2.1 can be used in combination with the pressure and von Mises stress todetermine if an element is inside the initial yield surface (F < 0), or outsidethe initial yield surface (F > 0) which implies yielding of the material. Asthe foam is very brittle in tension, the points at which the pressure stress ispositive (left of the q axis) are of most importance in determining yieldingwhich leads to cracks in the foam. Therefore the elements which show anegative pressure for the first time are examined carefully. When done sothere are four elements on the top of the block which fit the criterium. Thefour elements are displayed in figure 3.9.

Figure 3.9: Elements having negative pressure (tensile state) in the 2009model

For each of the four elements, F is calculated as a function of the time. Theresults are shown in figure 3.10.



Figure 3.10: F as a function of time

These graphs indicate that the value of F becomes positive at 57 ms. Thisis the step at which the four elements displayed in figure 3.9 were identified.It is therefore assumed that the foam will start to fracture at the place ofthe four elements. This is consistent with the footage of the actual crashtest done in 2009, which showed that a crack developed through the middlefrom the front to the back as can be seen in figure 3.11.

Figure 3.11: Crack initiation (right to left) during crash (top view)



Finally, the deceleration values of the simulation can be compared with thedeceleration values measured during the crash test done in 2009. The resultsare depicted in figure 3.12.

Figure 3.12: Comparison between the deceleration values calculated withAbaqus and the 2009 crash test

The two graphs approximately match in the beginning. At the end however,the two graphs start to differ. This is because the Abaqus model is notequipped with a failure model and thus fails to model the crack propagation.It can be concluded that the model is only valid up to the point where theyield strain in tension is reached locally.


Chapter 4

New design

4.1 Design requirements

The design of the formula student front impact attenuator needs to complywith certain rules. There are rules which specify the dimension of the frontimpact attenuator and there are the rules specifying the function of theimpact attenuator [04]. The most important rules concerning the researchare B3.20.1 which states that the attenuator must occupy a space of 200 mmx 200 mm x 100 mm (l x w x h) in front of the car and rule B3.21.1 whichstates that the attenuator must be able so stop a mass of 300 kg travelingat a velocity of 7 m/s with a maximal deceleration of 40g and a maximalaverage deceleration of 20g.

4.2 Foam shapes

4.2.1 Geometry

The first test was done with the minimal dimensions specified by the rules.Again two analytical rigid planes were used. This time however, the analyt-ical rigid plane resembling the front of the car was put at a ten degree angleof vertical to properly model the current design of the front of the car. Apoint mass was added to resemble the required 300 kg weight. The collisionwas modeled using the 7 m/s velocity. The model used is depicted on theleft in figure 4.1.

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Figure 4.1: Numerical model having the minimal dimensions as specifiedby the rules, initial shape on the left and deformed on the right

The problem with the minimal dimensions is that due to the anti intrusionplate which is at an angle, the front impact attenuator is subject to buckling,which is shown on the right in figure 4.1. As Rohacell 110IG foam is verybrittle in tension and when the foam specimen is subject to buckling, itwould be certain the foam would break and probable that the foam wouldmove beneath the front of the car making it unusable for energy absorption.

A solution to this problem would be to change the angles between the antiintrusion plate and the top and bottom of the foam block which can be seenon the left of figure 4.2.

Figure 4.2: Foam specimen with adjusted angles, initial shape on the leftand deformed on the right

Although in the new situation the specimen will yield, the foam block willnot buckle. Instead, the foam will collapse in the direction of the movement,shown on the right of figure 4.2. This ensures that the foam will not moveout under the anti intrusion plate during the crash.

In order to investigate the effect of this geometrical adjustment, angle θ isintroduced in figure 4.3.



Figure 4.3: Introduction of angle θ to describe the geometry of the newdesign

During the simulations, only this angle will be varied. If angle theta increaseswith 1 degree the mass of the foam block increases with about 14 gram. Asthis is less than 3 percent of the total mass of the foam block, this increasein weight is neglected. This means the time at which the yield criteriumin tension is reached can be used as a parameter to compare the differentmodels, while at the same time give an indication of the amount of damagea particular foam specimen with the corresponding angle will have. Angleθ has been varied from 0 to 6 degrees and the same damage criterium as inparagraph 3.3.2 was used. The results are shown in figure 4.4.

Figure 4.4: Time until fracture as a function of angle θ

The results shown in figure 4.4 indicate there is a minimum at three and fourdegrees, which means those foam specimens will fracture more easily withrespect to specimens with other angles. One important remark concerningfigure 4.4 is that only the specimen with θ equal to zero will buckle.



4.2.2 Anti intrusion plate

As indicated in paragraph 4.2.1, a foam specimen with θ equal to zero willbuckle easily. This is caused by the anti intrusion plate which is placedat an 10 degree angle off vertical. In this paragraph, a simulation will bediscussed where the anti intrusion plate is vertical and the foam specimen hasthe minimal dimensions as explained at the design requirements. In essence,this model is the same as the one used for the simple collision model shownin figure 3.2. If the damage criterium discussed in paragraph 3.3.2 is usedand the pressure and the von Mises stresses are examined, then the resultsindicate that there will be no damage in the foam specimen as the pressuredoes not become negative throughout the simulation. If there is no damage,then the model will be an accurate representative of a real crash test, whichimplies that the deceleration graph also will be a valid representation of thereal deceleration. The deceleration graph of the model is shown in figure4.5.

Figure 4.5: Deceleration for the model with the vertical anti intrusionplate model

Figure 4.5 indicates that the deceleration requirements specified by the for-mula student organization would be easily met. The peak deceleration isbelow 200 m/s2 and therefore the average deceleration is also below 200m/s2, whilst in order to comply with the rules, the maximal peak deceler-ation is limited to 40g and the maximal average deceleration is limited to20g.


Chapter 5

Conclusion andrecommendations

5.1 Material

The Rohacell 110IG foam has proven to be a very brittle foam in tension,which can be used as an energy absorbing material. When evaluating thesimulation done with the 2008/2009 foam specimen and the simulation donewith the minimal dimensions specified by the formula student rules and thevertical anti intrusion plate, it becomes visible that the attenuator made outof the Rohacell 110IG foam passes the test easily.

5.2 Geometry

5.2.1 Anti intrusion plate

When considering the tests done, it can be concluded that the anti intrusionplate placed at an angle has a negative effect on the crash in the sensethat the foam specimen will fracture. Simulations done with a vertical antiintrusion plate indicate that there would be no fracturing of the foam whichleads to an improved accuracy of the results.

5.2.2 Foam geometry

When evaluating the foam specimens intended to fit the design space (withthe anti intrusion plate at an angle), it can be concluded that an impactattenuator with a positive angle θ is preferable over a specimen with angleθ equal to zero. When varying angle θ, the time it takes until the specimen

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fractures varies and shows a minimum at 3 and 4 degrees. When evaluatingthe foam specimen attached to the vertical anti intrusion plate, it can beconcluded that there is no damage and that the deceleration would meetformula student standards.

5.2.3 Research method

This research has presented a way to model the continuum behavior of Ro-hacell 110IG and a way to determine if a foam specimen wil fracture or not.If the foam fractures, the place of the initial fracture can be determined.The yield criterium has proven to work as can be seen with the 2008/2009simulation. Furthermore the research method used in this report was able toglobally reproduce the deceleration graph of the 2008/2009 test. In the caseof a vertical anti intrusion plate, the model used in this research indicatedthat the foam would nog fracture. This would mean that the decelerationgraph of this model would be an accurate representation of a real crash test.

5.3 Conclusion

With respect to the main goals of this thesis it can be said that the im-plementation of a material model to investigate changes in a continuum ofthe foam was a succes. Furthermore the research has used a yield criteriumwhich accurately predicts the point of fracture of a foam specimen, if thereis one. This yield criterium was verified with the 2008/2009 crash test.While evaluating different foam geometries, this research has proven thatthe current design of the anti intrusion plate is not the best one and thatthe design with the vertical anti intrusion plate is the best one. With respectto the weight optimization, it can be said that the model is optimized in thesense that a minimal angle θ is indicated at which the foam does not buckle.Together with the fact that the angle θ was implemented on the minimaldimensions specified by the rules, the minimal dimensions of a valid andstable front impact attenuator are determined.

A point of criticism that can be made is that there was no damage modelimplemented, and therefore the behavior after fracture is an indication andnot 100% reliable.

5.4 Recommendations

The recommendations that can be done based on this research are the factthat the anti intrusion plate should be placed vertical when designing anext generation formula student car because this would improve the collapse



of the front impact attenuator in the sense that there would not be anybuckling.

With respect to the material used it can be said that the Rohacell 110IGfoam easily met the formula student standards, so research should be doneto investigate if lighter materials also would be sufficient. A second recom-mendation regarding the material used would be to investigate if materialscould be used which are not as brittle in tension as Rohacell 110IG foam.

The material model used did not include a damage model. To enhance theaccuracy of the simulations after the foam fractures, a damage model isnecessary.


Appendix A: Foamdimensions

Figure 5.1: 2008/2009 foam dimensions ([mm])

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Bibliography

[01] Deshpande, V. S., and N. A. Fleck, Isotropic Constitutive Modelfor Metallic Foams, Journal of the Mechanics and Physics ofSolids, vol. 48, pp. 1253 − 1276, 2000.

[02] Q.M. Li, R.A.W. Mines, R.S. Birch, The crush behavior ofRohacell-51WF structural foam, International Journal of Solidsand Structures, vol. 37, pp. 6321 − 6341, 2000.

[03] E.A. Flores-Johnson, Q.M. Li and R.A.W. Mines, ”Degradationof Elastic Modulus of Progressively Crushable Foams in UniaxialCompression”, Journal of Cellular Plastics, vol. 44, pp. 415−434,2008, DOI: 10.1177/0021955X08095113

[04] 2010 Formula SAE Rules, source: http://students.sae.org/competitions/formulaseries/rules/2010fsaerules.pdf, visited 28-9-2009

[05] Abaqus user manual version 6.8, Dassault Systemes S.A., 2005

[06] Rohacell data sheet, source: http://www.matweb.com/search/datasheet.aspx?matguid=a4736834d783413fb20601849248f115&ckck=1, visited 29-9-2009

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