Hamouda Journal 2005 1

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Materials & Design Materials and Design xxx (2005) xxx–xxx www.elsevier.com/locate/matdes

A new motorcycle helmet liner material: The finite element simulation and design of experiment optimization F.M. Shuaeib, A.M.S. Hamouda *, S.V. Wong, R.S. Radin Umar, M.M.H. Megat Ahmed Road Safety Research Centre, Faculty of Engineering, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia Received 5 January 2005; accepted 22 April 2005

Abstract This paper is devoted to study and verify the suitability of the expanded polypropylene (EPP) foam as a liner for motorcycle helmet and to perform helmet design optimization. This EPP foam has a multi-impact protection performance and also has a potential for ventilation system improvement due to its resiliency. This resiliency allows for the ease of ventilation holes and channels molding without the foam breakage at the stage of mold extraction. The large scale, non-linear, dynamic finite element package LS-DYNA3D is used as a verification tool for motorcycle helmet design. Then the simulation work is carried further to provide data for helmet design analysis and optimization using the response surface methodology (RSM). The foam thickness, the foam density, and shell thickness being selected as the design factors for the response surface generation and design optimization. The results showed that the EPP satisfies the 300g headform center of gravity acceleration limit required by most of the international standards. The extended simulation output data is then used to create the response surface and determine the optimum design points. Therefore, two main contributions on motorcycle helmet design are achieved. The first is on the use of the EPP as a helmet energy absorption liner for the motorcycle helmet application, and the second is that by combining the simulation output with the design of experiment (DOE) method to study the effects of the various factors on helmet design optimization.
2005 Elsevier Ltd. All rights reserved. Keywords: Design; Helmet; Simulation; Energy absorption; Foam

1. Introduction Helmets for motorcyclists are basically made form two main parts. The outer shell which is either made from thermoplastic material such as ABS or the polycarbonate, or composite material such as GRP or Kevlar. The inner liner, which is our focus here, is generally made from the expanded polystyrene (EPS) foam. This type of foam, in spite of its excellent first impact performance, has some essential performance deficiencies, which can be formulated as follows [9,10,23–25].

*

Corresponding author. Tel.: +603 89466330; fax: +603 86566061. E-mail address: [email protected] (A.M.S. Hamouda).

0261-3069/$ - see front matter
2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2005.04.015


EPS foam is a single impact performance and, from motorcycle crash kinematics studies it was evident that motorcycle crash is a multi-impact situation, particularly the most dangers high-speed crash.
EPS foam is brittle in its nature. This brittleness has led to two design problems, which is related to manufacturability. The former is the helmet roll-off due to the lack of fitness of the inside helmet contour, unless additional pads made from other resilient foams such as polyurethane are added in suitable locations. The later is the difficulty in introducing ventilation channels or ducts in the foam. This is important for countries with tropical climate including Malaysia. The expanded polypropylene (EPP) foam shows strong potential in overcoming such problems

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[9,20,12]. However its suitability as a motorcycle helmet liner needs to be thoroughly investigated from the mechanical performance point of view. Another objective which is included in this work is the helmet design optimization. This later objective was a challenging task in the previous research work due to the complex nature of the helmet structure and the various factors involved. Therefore, the two main objectives, which are targeted in this paper, namely; the verification of the EPP foam as a suitable liner for motorcycle helmet application, while the later is to develop helmet design optimization. The finite element simulation was the most suitable choice for such objectives, as once the design is found to be acceptable; the model parameters can easily be changed for parametric study. This is not feasible experimentally even if few EPP foam helmet prototypes where manufactured. This is because that any required change in the helmet design parameters needs some sort of modification to the molding facility, which is generally not feasible or extremely cost offensive. In the next paragraphs a brief review about the previous studies on the motorcycle helmet design and analysis is presented. At the early stage, solution of the helmeted-head impact problem was tackled either by experimental testing or by using analytical methods. The later techniques involves the development of simplified analytical models, which are composed of springs and dashpots to represent the helmet components. Then the analytical model is solved by basic dynamics methods. In the experimental investigation the results were restricted to varying the impact parameters such as the impact speed or the shape of the anvil. Varying helmet parameters experimentally were impossible due to testing sample manufacturing constraints. This had limited the benefits gained from the experimental studies to the standards requirements satisfaction. In the analytical solution, helmet impact on the crown against flat anvil was analytically modeled by Gilchrist and Mills [14]. The solution obtained, which is usually either one or two dimensional, had limited advantages due to the approximation involved and the disability of representing most of the essential impact features encountered in real accidents. The problem of helmet impact modeling and crash simulation is facilitated after the tremendous development in the computer technology and the development of the advanced simulation packages such as the LSDYNA3D [21] and the PAM CRASH [7]. Vetter et al. [30] conducted a finite element simulation of football helmet. Their study involves the simulation of helmet subjected to a static load on the crown. The effects of the variation of helmet structural and material properties were studied. Some principles of their research methodology can be utilized for dy-

namic simulation, which will have a more realistic meaning for motorcycle helmet crash studies. Yetham et al. [31] have developed a simplified finite element model for studying motorcycle helmets using LS-DYNA3D code. They model the impact of a helmet fitted on a wooden headform. The headform was given a simplified spherical shape, while the helmet was given a hemispherical shape. Various types of helmet shell materials were used in the analysis, such as GRP, PC, and LDPE. However, the widely used ABS shell material was not considered. Three densities of EPS foam were used. Their study has provided an excellent start of motorcycle helmet simulation and parametric studies using the finite element simulation techniques. Recently, Liu et al. [20] carried more advanced helmet crash simulation using the same LS-DYNA3D code. They have used ABS material for the shell and the EPS foam as the helmet liner. Their main concern was to develop a helmeted-head finite element model and carry out a validation process rather than performing parametric studies or optimization. The mechanical properties for these components were obtained experimentally under quasi-static conditions. Their simulation was carried out using both standard headform model and biomechanical head model. The impact site was rotated between the front to the back of the helmet. The heights of impact simulated were relatively small, and not conforming to any well known helmet testing standards. However, their study is another essential step in this field. In our study the previously described modeling techniques can be considered in the development of the EPP foam liner helmet model. The material model will be different from those models utilized for the EPS. In this study the finite element method is used for the helmet impact solution. The choice of using the finite element method is taken because of its capability to analysis metal and non-metal structures in an accurate way, and its availability as a finite element package (such as LS-DYNA3D), coupled with easy access to the required computing resources. The design analysis and optimization is performed using the response surface method (RSM) in the design of experiment (DOE) statistical methods. This method is easy to apply and provides a comprehensive overview on the factors effecting a targeted response [27]. Also it is the only method to investigate interaction effects between the considered factors [28]. This method is extensively used for experimental work, and its use for simulation oriented research work is a recent trend. In this regard, few programs are recently developed that uses the RSM with the finite element simulation as a predicted response. Among those are the LS-DYNA-OPT [21]. Therefore it is selected in this research work to perform helmet design analysis and optimization.

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2. The research methodology The methodology followed in this study is shown in the flowchart of Fig. 1. First, in order to model the helmet components, the material properties for each component needs to collected. Then helmet model can be built using Hypermesh pre-processor. After model translation to LS-DYNA3D, the helmet model impact is simulated using LS-DYNA3D finite element solver; the output is displayed using both LS-DYNA3D Finite Element Model Builder (FEMB) for the basic results visualization and the Hypermesh post-processor [1] for more detailed display features. The simulation results are categorized to two types. The first is the helmet design verification simulations while the second is the response surface DOE simulations. In the former the model is checked against the Malaysian helmet standard MS 1: 1996 which quotes the 300g peak acceleration limit of the headform center of gravity. However, this limit is the same for other international helmet standards such as the British standards BS 6658: 1985 [3]. In the later simulations, the impact anvil is kept to the flat type and the helmet design parameters are varied according Start Data Collection Model Building Pre-processing ( Hypermesh program )

Standards verfication simulation

Processing

Simulations required by the RSM

(LS-DYNA3D program) Post-processing

DOE Response surface creation

Response surface optimization

to the response surface method requirements. The peak linear acceleration, which is the predicted response in the DOE, is recorded in each case. The simulation data are inserted in the response surface design matrix, then the response surface is created. After the response surface creation, the surface can be analyzed, and the 3 D response surface and contours can be plotted. Also optimization process can be performed. In this research work both tasks are performed to have a comprehensive helmet design analysis and optimization. Results are then discussed, and conclusions are withdrawn.

3. Material properties Modeling of the complete helmet requires the input data of the constituentÕs materials of the helmet. As mentioned previously, the two main components of the helmet are the shell and the liner. As the target in this study is the energy absorption of the new foam candidate, the shell material is selected to be the current market dominant shell material which is the ABS. This material has good impact properties, and possesses a cost effective manufacturing method. It has some draw back which is discussed elsewhere under the same research program [9,10]. The use of this material allows for comparing results with helmets made from the same shell material and the current EPS foam liner with more accurate judgment than composite shell. The liner is the material under investigation which is the EPP foam. The EPP foam can be manufactured with the bead molding process as for the EPS. Therefore, the most crucial liner design constraint which is the manufacturability is eliminated from the comparison, and more realistic judgment can be made on the mechanical performance. 3.1. Mechanical properties of ABS material

(FEMB, GRAPH, Hypermesh programs)

Results and discussion

3

Response surface analysis

Results and discussion

Conclusions

End

Fig. 1. The flowchart for the research methodology.

To model the ABS material, the stress–strain behavior is required. Therefore, three specimens cut from helmet shells supplied by local manufacture (SolidGold) [29], and another three cut from flat ABS sheet supplied by industrial hardware supplier (FARNELL) [8] are tested in tension. The helmet specimens were not completely straight, and no any measure is made to straighten them as it is believed that any mechanical or thermal treatment may alter the mechanical properties of the specimens. The helmet specimens are cut from the sides of the helmet shell where they have the least curvature. Then the slightly curved specimens are inserted to the Instron universal testing machine, where they have been straightened during fixing and jigs clamping. The tests are carried on quasi-static strain rate of 60 mm/min which might be the reason behind the relatively fast breaking points of the tests specimens. As shown in Fig. 2 the behavior of the experimental test results and

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Stress MPa

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F.M. Shuaeib et al. / Materials and Design xxx (2005) xxx–xxx 40 35 30 25 20 15 10

X f ¼ X s Un ;

Farnnel Helmet Dean&Read

5 0

0

0.05

0.1

0.15 0.2 Strain %

0.25

0.3

0.35

Fig. 2. ABS experimental tensile stress–strain curves. The first is for a flat plate cut from ABS sheet produced by FARNNEL Company, the second is specimens cut from SolidGold helmet shell, while the third is the literature data [6].

other published test results [6] are very close particularly in the yield stress, and the youngÕs modulus. Therefore the general trend of later data are considered for the region beyond the tested range. 3.2. Mechanical properties of EPP foam The quasi-static mechanical properties of the EPP foams are reasonably available in recent publications, whereas impact properties are very limited [13]. This might be attributed to the fact that low density EPP foam type is newly developed and not much literature is published on its characteristics. As the required data of this type of foam is not sufficiently available in the literature, more detailed investigation and analysis is necessary. Accordingly the experimental data quoted by various references is described in Appendix A, and foam mathematical modeling theoretical review is also included in this work. Theoretical modeling: The mathematical approaches to model the static and dynamic behavior of the closed cell semi-rigid EPP foam are described. Typically, the EPP foam stress–strain behavior can be divided into three regions. The first region is the linear elasticity, the second is the non-linear or long plateau elasticity, and the third is the densification. Mathematical modeling of the first two regions is the most essential requirement for the foam finite element modeling. Therefore it will be descried in more details hereafter. The elasticity region: Theoretical modeling of the highly non-linear polymeric foams is still a wide area for further studies. Most of the previous work was carried out for the static behavior of foams. Many empirical and semi-empirical equations have been developed, and some of which are applicable for certain foams and under specific conditions [13]. Eq. (1) is a simple and widely used relation which predicts the elastic mechanical properties of EPP foam. This equation correlates the mechanical properties of the foam to the density. For mechanical properties Xf (strength, modulus, etc.) a power law relationship has been found to apply in most cases

ð1Þ

where U is the relative foam property with respect the solid-state property. ‘‘Xs’’ refers to the property of the solid matrix parameter and the exponent ‘‘n’’ depends on the property in equation. It is usually lies in the range of 1.0 < n < 2.0 and for the closed cell EPP foam it takes the following values: for strength = 2, for modulus = 2, and for the shear stress = 1 [13]. The non-linear elasticity region: Linear elasticity is limited to small strains, typically 5% or less. The EPP foam can be compressed much larger than this. The deformation is still recoverable (and thus elastic), but it is non-linear. In compression the stress strain curve shows an extensive plateau stress starting form O0el the elastic collapse stress. This elastic collapse is caused by buckling of cell walls. For the closed cell EPP foam the compression of the gas within the cells, together with the membrane stresses, which appears in the cell faces, gives a curve of stress which rises with the strain. At present a general model, which predicts all the effects for the EPP mechanical behavior does not exist. This may be due to the complex nature of the foam behavior and the large number of factors, which affect its behavior. Factors such as density, temperature, strain rate, and manufacturing process are found to have a greater effect than others [13,14]. A theoretical expression for the yield stress increase based on cell gas compression was initially developed by Rusch [11] for closed cell foams and then verified by several researchers ([13,26]). This expression uses the isothermal compression of the air in the closed cells. The gas in the cells obeys BoyleÕs law, initially its at the atmospheric pressure of p0 = 0.1 MPa (1 atm) and it occupies a fractional volume (1-D) of the foam. When the compressive strain is e the gas in the foam exerts a pressure p on the loading surface equals to: p0 e . ð2Þ p¼ 1eD If there is also a constant contribution of r0 to the yield stress due to the compressive buckling of the cell elements, the compressive stress is given by r ¼ r0 þ

p0 e . 1eD

ð3Þ

The gas pressure contribution explains part of the stress increase at higher strains. Mills [24] reported that by plotting the compressive stress for polyfin foams such as expanded polypropylene, or polyethylene against the strain function (the right part excluding r0) in Eq. (3) above, the slope p values ranges from 0.08 to 0.2 MPa. The high pressure values can be explained by saying that other processes, such as induced cell face tensions, are equivalent to the foam being filled by a gas at a pressure

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greater than atmospheric. It means that the parameter p in Eq. (3) must be treated as a curve fitting constant, and therefore its necessary to find its value as a function of the foam density for each range of foams. Recently, Mills and Gilchrist modeled the impact of the BASF EPP foam with Eq. (3) [26]. The foam density range used is 20–90 kg/m3, and the gas pressure is 0.2 MPa. There results from the mathematical model show good correlation with the experimental results. Therefore, the same approach is used in this research and stress–strain curves for EPP foam are generated using Eq. (3) and the results are shown in Fig. A.1(a) of Appendix A. As can be noticed the theoretical curves reasonably well approximates the BASF experimental results of Fig. A.1(b) and also very close to reported data by Mills [24] which is shown in Fig. A.2 of Appendix A. These results are also found to well agree with data published by other researchers for the same type of foam [5].

4. Finite element modeling and simulation The finite element simulation aspects for helmet impact are presented here. At the beginning the simulation tools are described, then the helmet components modeling are presented and discussed. Afterwards, the complete helmet model is verified against the helmet standard and simulations are extended for the response surface DOE requirements. Simulation tools: Finite element simulation of structural problems involves three basic steps. The first is the pre-processing step; then the analysis step; and the post-processing step. In this study, the Hypermesh computer code has been used for the first step. Hypermesh is part of the hyperworks finite element package produced by Altair Engineering. This program is a high performance finite element pre and post processor that enables the user to generate finite element models for engineering simulation and analysis. The analysis step involves the non-linear transient prediction for dynamic behavior. The LS-DYNA3D has been used herein. Finally, the Finite Element Model Builder (FEMB), GRAPH, and Hypermesh are used for post processing the results. LS-DYNA3D is a large-scale non-linear finite element package [18]. This code performs a non-linear transient dynamic analysis of three-dimensional structures. Originally developed by DYNA3D-family of computer codes at the Livermore National Laboratory, LS-DYNA represents the commercial version of these codes and is available through the Livermore Software Technology Corporation [21]. LS-DYNA has a wide variety of analysis capabilities including a large number of material models, a variety of contact modeling options, a large library of beam, plate, shell, and solid ele-

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ments and robust algorithms for adaptively controlling the solution process. The transient analysis is performed using an explicit direct time integration procedure and thereby avoids the need for matrix evaluation, assembly and decomposition at each time step as required by many implicit time-integration algorithms. LS-DYNA automatically examines the finite element mesh and material properties in order to determine an appropriate time step size for numerical stability. This time step size is then automatically adjusted throughout the transient analysis to account for contact local material and geometric non-linearities. 4.1. Finite element modeling of ABS shell material According to test results described previously for the ABS shell material, the stress–strain data are averaged taking into consideration the test results of the helmet, the FARNNEL flat plate specimens and also literature test results [6]. These data is then converted into true stress and strain values as required by material model M-24, linear piecewise plasticity model of LS-DYNA3D materials library. The selection of this model is recommended by the LS-DYNA3D user manual for crashworthiness applications and also used by other researchers for the same ABS material [20]. The results are shown in Table 1. 4.2. Finite element modeling of EPP foam liner In order to model and validate this type of foam the experimental impact test results of Chou et al. [5] and the stress strain input data of Eq. (3) are used in this work. Chou et al. experimental test results involves the impact of a hemispherical aluminum headform of 4.5 kg weight on a cubical 63.3 kg/m3 EPP foam sample with the dimension of 254 mm · 254 mm · 76 mm. The impact speed is 6.7 m/s for the experimental test results, which is very close to the 6 m/s of the Malaysian standards speed requirement. The small difference between the two speeds is assumed to be negligible. Foam Model Selection: The low-density foam model M-57 of LS-DYNA3D material library is selected for modeling the EPP foam behavior. This selection is made according to LS-DYNA3D user manual and also used for polypropylene foam modeling by other researchers [4,5]. Furthermore, this model is found to be the most suitable among the other LS-DYNA3D foam models in terms of representing physical EPP foam behavior un-

Table 1 True stress and true strain of data for tensile test of ABS material used in shell modeling True strain True stress

0 0

0.0174 35.6

0.0371 32.17

0.095 34.6

0.182 37.8

0.26 44.2

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der compression and simplicity of input data. This model requires uniaxial stress–strain data and other parameters, which can obtained by standard laboratory tests, unlike other foam models, which requires the dynamic pressure against volumetric strain experimental data and other parameters that is currently not available and/or difficult to obtain. Furthermore, helmet impact condition involves mainly a uniaxial compression loading. This is also confirmed by Gilchrist, and Mills who had large contribution in helmet and foam studies [16]. Foam Modeling and Validation: Upon simulation trials of EPP foam using this model, it is found that the impact stress–strain curve needs to be calibrated in order to fit the experimental results. The most sensitive parameter found to be the collapse stress, which is in some references termed the yield stress. The slight tuning of this parameter has a little change on the overall shape of the experimental foam stress–strain curve, but it considerably affects the simulation peak acceleration results. The EPP foam is modeled using solid hexagon element type with full integration points to avoid hourglassing effects as recommended by the user manual for components that undergoes large deformations [18]. The general automatic contact type is used to model all contact surfaces in this validation model. The contact stiffness has to be scaled up to avoid significant penetration of the element edges between the contacted parts. The element type selected for the headform is also solid hexagonal type with single integration points. The material of the headform is aluminum, which is modeled using the elastic material model M-1 of the LS-DYNA3D material library. The stiffness of the model is increased to avoid headform elastic deformation, which may interfere with the foam energy absorption results. A rigid material can be selected, but the contact with elastic materials is more stable. Fig. 3(a) and (b) shows the model used and the validation results, respectively.

The good correlation can be clearly seen between the experimental and the simulation results. 4.3. The helmet finite element modeling The task here is to model the complete helmet–headform system and impact anvil. This model will be used for impact simulation of the helmet design verification and also fore response surface design analysis and optimization. Some of the geometrical details, which are generally meant for other than mechanical performance requirements such as aerodynamics and styling, are omitted in this study. This is also necessary because response surface analysis and optimization requires the generation of many complete helmet models with different helmet parameters. Therefore building excessively detailed model for each simulation run will make this job completely tedious and not practical to perform. This computational helmet–headform model consists of a hemispherical aluminum headform, the EPP foam liner and the ABS shell. The headform used has a hemispherical shape. Several materials can be used for headform such as magnesium, aluminum, or hardwood (MS1 1996, and BS 6658:1985). As experimental test results for aluminum headform impact is currently available which is used for EPP foam model validation explained previously, it is used in the helmet–headform simulation model. The headform, and the foam liner are modeled using hexagon solid element type of the LS-DYNA3D element library, while the shell is modeled using the thick shell element type. Table 2 shows modeling details of the complete helmet system under consideration. The helmet models are shown schematically in Fig. 4(a) and (b). Two types of anvils are used in helmet design verification. The first is circular flat with diameter of 125 mm, while the second is hemispherical shape with 50 mm radius. These types of anvils are typical for almost all mo-

Fig. 3. The EPP foam model validation.

ARTICLE IN PRESS F.M. Shuaeib et al. / Materials and Design xxx (2005) xxx–xxx Table 2 Finite element model details Component

Material

Element type

Headform Foam Shell Flat Anvil

Aluminum EPP ABS Steel

Solid Solid Thick shell Solid Total

No. of elements 330 564 564 252 1710

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the shape of the flat anvil impact curve for uniform shell and liner deformation. As shown, the model predicts lower peak acceleration value for the hemispherical anvil impacts compared to the flat anvil. This might be attributed to the ABS shell local buckling, which led to more shell and liner energy absorption contributions. This is a positive point in EPP lined helmet design, as the helmet design for flat anvil which is the most frequent impact shape [14] will be more conservative for hemispherical and other similar objects. However, this finding cannot be generalized for all shapes as very sharp object will result in different mode of helmet failure and the acceleration limit criteria will not be applicable. This suggests that if a precise effect of the impactor shape is needed a further study on this particular item might be performed. In summary, the previous results proved that the use of the EPP foam as a helmet liner is found to satisfy the helmet standards in terms of the peak acceleration. The general acceleration trend is similar to the EPS lined helmet. Therefore these results encouraged the authors to extend the simulation work to cover the helmet design analysis and optimization using the response surface method. This method is explained in the next section.

Fig. 4. The finite element helmet models used in the simulation.

5. Response surface DOEs analysis and optimization torcycle helmet standards. The impact speed is 6 m/s. The liner and shell thickness are 25 and 5 mm, respectively. The thickness is selected according to the current helmet design with plastic shell and EPS foam liner. This will allow for meaningful comparison between the new and existing designs. The result of the simulation is shown in Fig. 5(a) and (b), and discussed in the following section. 4.4. Discussion of the computational results In general, from the simulation output results shown in Fig. 5(a) and (b), it can be observed that this helmet design which uses the EPP foam as a liner satisfy the Malaysian Standards MS1: 1996 [22] requirements, which is the 300g-peak acceleration limit. This limit is almost the same for most of the well-known international helmet standards. For the flat anvil the peak acceleration is about 235g accruing at about 6.5 ms. The total impact duration for the flat anvil impact is about 11 ms. This is of similar trend compared with the EPS lined helmet from both the peak acceleration and impact duration [14,15,20]. For the hemispherical anvil there are two peaks. The first is equal 150g occurring at 2 ms and has a sharp drop, which might be due to shell buckling and element instability might be the reason behind the very sharp tip of the curve. The second is equal to 140 occurring approximately at 7 ms. The peak is smoother and takes

5.1. Theoretical background Response surface methodology is a collection of statistical tools and techniques used for constructing an approximate functional relationship between response (calculated and/or measured phenomenon) and design variables (a number of independent factors or variables that affect the response) [17,27,28]. The approximate function relation, typically in the form of low order polynomial, is referred as the response surface. Response surface approximations were originally developed for fitting data from physical experiments. However, in our case the physical experiments are replaced with the simulation results. This approach is becoming increasingly popular in recent years which may represent a mile stone in mechanical design analysis and optimization. The response surface serves the purpose of filtering the noise and providing the designer with a simple surrogate model to describe the response. The relationship between the response (y) and the independent variables (x) can be expressed using a mathematical model of the general form, y ¼ f ðx1 ; x2 ; . . . ; xn Þ þ e;

ð4Þ

where e is the ‘‘total error’’ (that is the difference between the actual values and the predicted values) and n is the number of the predictor variables in the model.

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Fig. 5. The results of the helmet impact simulation using the EPP(65 kg/m3) foam. (a) Headform CG acceleration for helmet impact on flat anvil. (b) Headform CG acceleration for Helmet impact on hemispherical anvil.

The function f(x) is normally chosen to be a low order polynomial, typically linear or quadratic. A quadratic model may be represented mathematically as follows: X X y ¼ b0 þ bi xi þ bij xi xj ; ð5Þ i

i<j

where bÕs are the coefficients that describe the response function. The estimated coefficients of the fitted model will be denoted by b, for n variables, the quadratic model equation (5) has a total of p = (n + 1)(k + 2)/2 coefficients. Response surface construction: If f(x) accurately describes the process being modeled, e may be considered as a random error, often assumed to have a normal distribution with zero mean. In this case f(x) is an unbiased estimate of y and e accounts for sources of variation not accounted for by f(x), but which are still inherent to the process such as noise and measurement errors.

Once the model to characterize the response is selected, then the coefficients b0. b1, bn will have to be estimated. Typically, a least squares method that minimizes the error residual is utilized for estimating the coefficients of the model equation [27]. Response surface DOEs: RSM has methods for selecting data points at which the response function should be evaluated. The procedure of choosing a small set of optimal points in the design space to fit the approximation is termed ‘‘design of experiments’’. The design points are chosen to maximize the predictive capabilities of the response function. In cases where there are significant noise (variance) errors, the points are chosen such that they minimize the variance error in the fitted coefficients. For problems with small numbers of design variables in regularly shaped domains, selection schemes, called standard designs, are available. In the present research the standard DOE scheme is adopted. The former is the central composite experi-

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ment, and the later is the Box–Behnken designs. The features of each schemes is highlighted in the forthcoming paragraphs and a selection of the most suitable scheme for this research is made. Central composite designs: Central composite designs are often recommended when the design plan calls for sequential experimentation because these designs can incorporate information from a properly planned factorial experiment. The factorial or ‘‘cube’’ portion and center points may serve as a preliminary stage where a first-order (linear) model can be fitted, but still provide evidence regarding the importance of a second-order contribution or curvature. Central composite designs usually have axial points outside the ‘‘cube’’ (unless  parameter is specified that is less than or equal to one). These points may not be in the region of interest, or may be impossible to run because they are beyond safe operating limits. Central composite designs also allow for efficient estimation of the quadratic terms in the second-order model, and it is easy to obtain the desirable design properties of orthogonal blocking and rotatability. Orthogonally blocked designs allow for model terms and block effects to be estimated independently and minimize the variation in the regression coefficients. Rotatable designs provide the desirable property of constant prediction variance at all points that are equidistant from the design center, thus improving the quality of the prediction. Box–Behnken designs: Box–Behnken designs are generally recommended when performing non-sequential experiments. That is, when planning to perform the experiment once. These designs allow for efficient estimation of the first and second order coefficients. Because Box–Behnken designs have fewer design points, they are less expensive to run than central composite designs with the same number of factors. Also, Box–Behnken designs can prove useful if the safe operating zone for the design under consideration is known. Box–Behnken designs do not have axial points, thus, all design points will fall within the safe operating zone and also Box–Behnken designs ensure that all factors are never set at their high levels simultaneously. 5.2. The response surface solution According to the above reasons, and due to fact that simulation results are constant response results and either randomization or replication will not alter the response. Therefore, the most economical design scheme which is the Box–Behnken design is adopted in this research program. In the next paragraphs the procedure followed in the response surface solution is described. The response surface design factors and their levels: For the response surface to be created the design factors and their levels need to be specified first. The three de-

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Table 3 The response surface design levels Level

Foam density (kg/m3)

Foam thickness (mm)

Shell thickness (mm)

(1) Low (0) Medium (+1) High

45 55 65

15 20 25

3 4 5

sign factors considered in this helmet design research are, the foam density, the foam thickness, and the shell thickness. Their levels are estimated based on several factors. Among those are the current helmet designs with EPS foam liner, and some simulation trials with EPP foam as a liner. The factors and their design levels are shown in Table 3. Response surface creation and analysis: After the design factors and their levels are set, the DOE matrix based on the Box–Behnken method is created. The finite element helmet model parameters are then varied according to the DOE matrix settings. Crash simulation is carried out for each design point (helmet model) and the peak linear acceleration (response) is recorded and keyed into the design matrix as appropriate. When all data are completed the response surface is analyzed. The full quadratic model is selected to analysis the response surface. This model is selected because few variables are involved in this study and the selected model will allow for the detection of even small curvature in the response surfaces. This is beneficial for more detailed investigation of the parameters effects. The output results are generated in the form of three dimensional response surface plots and contour plots. The discussion of these results is given in the next section. 5.3. Response surface results and discussion The response surface design matrix with the simulation results keyed in is shown in Table 4 and the response surface graphs and contour graphs are shown in Figs. 6–11. Each graph have the peak linear acceleration ‘‘ACC’’ as a response parameter plotted against two of the three helmet design factors, which are the foam density ‘‘ROW’’, the foam thickness ‘‘T-foam’’ and the shell thickness ‘‘t-shell’’. Fig. 6 shows the peak linear acceleration in gÕs plotted against the foam thickness and the foam density. As can be seen, the curve has a smooth slope upward in the foam density face, while it show a steeper downward curve for the foam thickness effect face. Investigating each parameter at a time, so considering the foam density effect, the acceleration has a value of about 275g at the lower foam density level of 45 kg/m3. Then, the acceleration starts to smoothly increases as the foam density increase until reaching to about 290g at the 65 kg/m3 end. This might give impression that if the

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Table 4 Data Matrix in coded units (randomized)

Contour Plot of Acc

Row

T-foam

t-shell

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0 +   + 0 0 + 0 0  0  0 +

0 + 0 +  0 + 0   0 +  0 0

0 0 + 0 0 0    +  + 0 0 +

25

230 250 270 290

24 23 22

T-foam

Run

21 20 19 18 17 16 15 45

55 Row

65

Fig. 7. The contour plot of the acceleration against the foam thickness and the foam density.

Acc

Surface Plot of Acc

295 285 275 265 255 245 235 225 215 205

25 20

45 55

Row

65

T-foam

15

Fig. 6. The response surface of the acceleration against the foam thickness, and the foam density, ROW: Foam density (kg/m3), Tfoam: Foam thickness (mm), t-shell: Shell thickness (mm), Acc: Peak Headform CG acceleration (gÕs).

peak acceleration needs too be kept below 300g it will be necessary to keep the foam density below the 65 f kg/m3. This could be further investigated on the other graphs. Considering the foam thickness effects, as can be seen, the acceleration decreases as the foam thickness increase. The amount of decrease is quite considerable as compared to the foam density, which shows that the foam thickness effect is more important for lowering the acceleration level. However, for the selected thickness range, the observation is that there is no curve inversion (rise portion) as the foam thickness increase. This is expected as theoretically, by increasing the foam thickness, the acceleration will keep in decreasing, and no any reason will return the acceleration to the increasing stage again. Furthermore, to complete the analysis of these parameters effect on the acceleration, it is worth to in-

clude the contour plots for the same design parameters here. In this regard, Fig. 7 shows the contour plot of the peak linear acceleration against the foam density and the foam thickness. As shown by the constant acceleration lines, if the acceleration needs to be kept below 270g, then the foam thickness needs to be equal to or more than 17 mm for the foam density between 45 and 65 kg/m3. If the acceleration needs to be kept below 230g, the foam thickness needs to be equal to or more than 19.5 mm for foam density below 60 kg/m3. This type of plot can be very useful in design as once one parameter is specified the other parameter can be determined based on a given acceleration limit. Therefore both graphs had explored a significant part of helmet design. It is now required to have the same investigation of each of the previous factors with the shell thickness parameter. Fig. 8 shows the peak acceleration plotted against the foam density and the shell thickness. The significant effect of the foam density is evident as compared to the shell thickness. The shell thickness seams to have very little effect on the peak acceleration. This is clear from the shallow curvature of the response surface toward increasing the shell thickness. However, both the foam density and the shell thickness design values did not show any risk of approaching the helmet standard injury limit of 300g. This can be further investigated from the contour plots, which is presented hereafter. Fig. 9 shows the contour plot of the peak linear acceleration against the foam density and the shell thickness. As shown, from this curve less information can be obtained about the foam density effects. However, the shell thickness effects are more noticeable. This can be seen from the 232g and the 252g constant acceleration lines. For instance, if the 4 mm shell thickness with the corresponding foam density of 52.5 kg/m3, which is the curve inversion point, is considered as a reference point

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Surface Plot of Acc

Acc

250

240 230 5 220

4

45 55

65

Row

3

t-shell

Fig. 8. The response surface of the acceleration against the shell thickness, and the foam density.

11

Fig. 10 shows the response surface graph of the peak linear acceleration against the foam thickness and the shell thickness. As can be seen, the acceleration increased from about 220g to about 280g by decreasing the foam thickness from 25 to 15 mm. However, the shell thickness effect is of minor significance. This is evident from the small increase of the peak acceleration by increasing the shell thickness from 3 to 5 mm. These effects can also be observed from Fig. 11, which shows the contour plot of the peak acceleration against the foam thickness and the shell thickness. Again the shell thickness is of little importance in the performance response particularly at the lower foam thickness designs. In summary, the helmet design is thoroughly analyzed by the response surfaces and the contour plots generated. The two dominate factors seams to be the foam density, and the foam thickness, while the shell

Surface Plot of Acc

Contour Plot of Acc 5

232 242 252 280 260

4

Acc

t-shell

270 250 240 230 5

220 210

3

4 15

55 Row

Fig. 9. The contour plot of the acceleration response against the shell thickness and the foam density.

in the 232g line. Then, by decreasing the shell thickness to 3 mm, the density needs to be increased to 55 kg/m3 to lie on the 232g acceleration line. On the other hand, increasing the shell thickness to 5 mm needs that the foam density be increased to 55 kg/m3 to achieve the same result. From the previous it cab be concluded that the 4 mm and the 52.5 kg/m3 are the optimum setting for the 232g line. However, the situation is different for the 252g acceleration line, which is almost straight line. In this later line, changing the shell thickness dose not seem to have any effect on the foam density. So by comparing the two curves, we can conclude that the shell thickness effect is more evident for the lower density designs, than the higher ones. In general, this curve needs to be investigated in conjunction with other response and contour graphs to have a more comprehensive visualization.

t-shell

3

20

65

25

T-foam

Fig. 10. The response surface of the acceleration against the foam thickness, and the shell thickness.

Contour Plot of Acc 5

t-shell

45

230 240 250 260 270 280

4

3

15

16

17

18

19

20 21 T-foam

22

23

24

25

Fig. 11. The contour plot of the acceleration against the foam thickness and the shell thickness.

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thickness is of minor importance. This is agrees well with the helmet design principle as the function of the shell is to protect against penetration and basically is not considered for energy absorption. The next step required is to determine the optimum helmet design taking into consideration the three design factors all together. This is presented in the following section. 5.4. Optimal design For irregularly shaped design space, several computer-generated designs that are usually based on an optimality criterion are available. The best known among them is the D-optimal design. The D-optimal criterion minimizes the value of the variance error in the fitted coefficients. There are also other criteria available for selecting minimum variance design points (e.g., Aoptimality, G-optimality) that derived from minimizing other measures, such as trace error or maximum value of the diagonal [5,17,19,27]. Using the D-optimal method the results of the optimization are shown in Table 5, and discussed hereafter. Table 5 shows summary of the D-optimal design that was obtained by considering all the 15 points. The philosophy followed in this work is to include all the design points in the optimization solution. Obtain the optimum design points on a descending order of preference. Then select the most suitable first four alternatives. Therefore the four most attractive design alternatives are summa-

Fig. A.1. (a) The predicted EPP foam data plotted using Eq. (1). (b) The dynamic properties of BASF EPP foam for different densities [2].

Table 5 The D-optimal design matrix (Box–Behnken design) Order

Run order

Row

T-foam

t-shell

Peak acceleration (g)

14 4 7 3 2 15 10 6 9 11 5 12 1 13 8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

55 65 45 45 65 55 55 65 55 55 45 55 45 55 65

20 25 20 25 15 20 25 20 15 15 20 25 15 20 20

4 4 5 4 4 4 3 3 3 5 3 5 4 4 5

235 240 223 204 296 235 221 245 282 266 220 224 280 235 254

Table 6 The selected D-optimal design points Foam density (kg/m3)

Foam thickness (mm)

Shell thickness (mm)

Peak acceleration (g)

55 55 65

15 20 20

5 4 5

266 235 254

Fig. A.2. The dynamic stress strain curves for PP and rigid PU foam of various densities [24].

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rized in Table 6. It is to be emphasized here that these points are selected among the optimization results of Table 5. However the practical aspects of the current design is also taken into consideration. For example the 4 and 5 mm shell thickness designs are preferred to the 3 mm thickness designs due to other consideration such as the penetration resistance and shell rigidity. These selected points agreed well with the analysis made in the previous section.

6. Conclusions The main conclusions of this study can be summarized in the following points:
Current helmet design using the EPS foam as a liner material is not optimum considering the multi-impact performance, fitness and thermal comfort aspects.
EPP foam material is suitable for multi-impact, and has ventilation system improvements potential due to its resilience nature. Therefore, based on the finite element simulation, this foam material is investigated for the motorcycle helmet application. This EPP foam is found to be suitable energy absorption helmet liner according to Malaysian Standards MS1: 1996 [22] requirements.
A method to investigate the effects of helmet design parameters including the interaction effects between these parameters, and also to optimize helmet design is successfully developed. This method is based on the response surface technique of the DOE statistical method. The philosophy is that by using the finite element simulation results as a response in the response surface model the helmet design can be analyzed and optimum design determined. Furthermore, this method can effectively be used in further investigation of helmet design studies.
Based on the previous methodology solution, the foam thickness and the foam density are found to be the most contributing factors in preventing head injury represented by the peak linear acceleration limit of the 300g.
The shell thickness is found to be of minor importance from the energy absorption consideration.
The optimum helmet design using the EPP foam as a helmet liner is found to be a helmet with 55 kg/m 3 EPP foam density, 15 mm foam thickness, and 5 mm shell thickness.

Acknowledgement The financial support provided by the Ministry of Transportation, Malaysia is gratefully acknowledged.

13

Appendix A. See Figs. A.1 and A.2.

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