Performance of EVA foam in running shoes

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1 Performance of EVA foam in running shoes Raquel Verdejo and Nigel Mills Metallurgy and Materials, University of Birmingham, Birmingham, U.K Abstract: Both in-shoe measurements of plantar pressure, and Finite Element Analysis of the stress distribution in the heelpad and shoe midsole, were used to study the mechanics of heelstrike in running. The heelpad properties were deduced from published force-deflection data. The ASTM 1614 method of midsole testing produces significantly different peak pressures and stress distribution than does the human heelpad compressing an EVA foam midsole. Midsole deterioration was measured in controlled running tests, and air loss from the foam shown to cause reduced heelstrike cushioning. INTRODUCTION Running involves a series of heel-strike impacts on the ground. The midsole foams of running shoes, by absorbing energy, limit the peak impact force in the heel-strike. In the course of a long run, there is a reduction of the air content of the foam cells, reducing the cushioning. The foam does not appear to fully recover after a run. The foamed copolymer of ethylene and vinyl acetate (EVA) is widely used in running shoe midsoles. The density of the closed-cell, crosslinked foams ranges from 150 to 250 kg m -3. Misevich and Cavenagh (1984) performed repeated rapidcompression tests on EVA foam - in these the stress was constant through the foam. They showed that the midsole force-deflection response changes with cycle number. They claimed there was an initially positive internal gas pressure in the foam cells; this declined during repeated loading, as air diffused through the cell faces. Barlett (1995) discussed the cell geometry seen in sectioned EVA midsoles, claiming that cells next to the outsole became flattened after 3200 km of running, and that some cell faces fractured while others buckled. Mills and Perez (2001) modelled creep loading of EVA foams, showing that gas diffusion contributed significantly to the creep process. However they did not consider the loading history experienced in a shoe. Sensor insoles can determine the pressure distribution on the upper foam surface, under the athlete s foot. Finite Element Analysis (FEA) is needed to analyse the large geometric changes in the heelpad and shoe foam, and to determine the stress field in the foam. Aerts et al (1995) described the force-deflection response of the human heelpad, while Gefen et al (2001) gave the mean pressure at the interface between the heelpad and a flat rigid surface as a function of an average heelpad thickness strain. However, they gave no heelpad stress-strain data. Thompson et al s (1999) FEA analysis considered the axially symmetric indentation of an EVA foam midsole by a rigid ASTM heelform, revealing some stress variation in the foam. However, there 1

2 has been no FEA of the stresses in a human heelpad, or its interaction with a shoe midsole. This paper performs such an analysis, and compares the results with experimentally measured foot pressure distributions during a run. MATERIAL CHARACTERISATION The midsole of the Reebok Aztrek DMX shoe was composed of EVA foams; a section of area 20 mm by 40 mm on the lateral side of the heel was coloured grey, and the rest white. The densities, measured using a hydrostatic balance were 170 and 173 kg/m 3 for the white and grey foams respectively, i.e. approximately the same. The foams were analysed with a Mettler Differential Scanning Calorimeter (DSC) 30. The degree of crystallinity was calculated by dividing the measured enthalpy of fusion by that for pure polyethylene (286.8 J/g). The results (table 1) are similar. Hence there is approximately 18 % VA in the copolymer. Table 1 Characterisation of EVA foams in Reebok midsole. Sample Melting Point (ºC) Melting Enthalpy (J/g) Crystallinity (%) White Grey PLANTAR PRESSURE DISTRIBUTION IN RUNNING Three healthy male long distance runners, aged 34, 37, and 49, weighed 91.4, 82.1, 63.4 kg, with UK shoe size 11, 9, 8 respectively. They were all rearfoot strikers, did not use orthotics, and reported no lower extremity injury for the past year. The study was approved by the University ethical committee. The Tekscan F-Scan system consists of a flexible, 0.18 mm thick sole-shape, having 960 pressure sensors, each 4 by 3 mm. The resistance of the pressure-sensitive ink, contained between 2 polymer-film substrates, decreases as the pressure, applied pressure to the substrate, increases (Ahroni, 1998). The sensor insole was trimmed to fit the subjects right shoe. It was calibrated by the known weight of the test subject standing on one foot. Data was recorded at 150 Hz for 4 sec. The subjects ran, at 2.61 m/s for 10 min, on a Quinton Instrument Co. 640 treadmill; this short experiment avoided fatigue. They wore trainers that were brandnew at the start of the experiment. The plantar distribution was recorded at the beginning, middle and end of the run. The subjects were asked to run on hard surfaces (track or roads) using the shoes for their training, and to keep a running distance diary. Every 15 days the plantar pressure distribution was measured, waiting 24 h since the last use to standardise the recovery time. They will run 500 to 1000 km using the shoes, then the cellular structure of the midsole will be compared with that in an unused pair of shoes, to investigate the foam damage. The Tekscan measurements show the in-shoe pressure distribution as a function of the running time. Figure 1 shows composite maps of the peak pressure at each pixel throughout the footstrike, at 1 and 10 minutes in a session. The peak pressures in the heel region (table 2) increased with run time in both sessions, with a greater increase in the second session, as result of prior use. The 1 minute peak pressures in the 2nd session are close to those in the 1st, due to the 1 day of recovery prior to testing. 2

3 Table 2 Peak pressures values (kpa) for the runners session first Distance second runner 1 min 5 min 10 min Run (km) 1 min 5 min 10 min Fig 1 Maximum pressures, at each sensor pixel, for footstrikes after 1 and 10 minutes. Repeat impact ASTM method. In this test a weight falls a fixed vertical distance onto the shoe midsole in the heel region (ASTM, 1999) with an impact kinetic energy of 5.0 J. The striker was the flat end of a steel cylinder of diameter 45 mm, with edge of 1.0 mm radius. The total drop mass of 5.9 kg fell 85 mm, guided by low friction bearings on 2 vertical cables. The signal from an accelerometer on the striker was captured digitally and analysed by computer to give the striker force versus the deflection of the top surface of the midsole (Mills, 1994). The outsole was removed from the shoe heel giving a flat surface, which was fixed to a horizontal rigid fixed anvil. The midsole thickness was 20.1 mm. Data were collected from the first and the 26 th impact. The sample was allowed to recover for 15 min, and 100 cycles were performed on it, recording data every 25 cycles. The foam force-deflection was studied as a function of time. Table 3 shows how the peak deflection and force increase slightly with impact number, while the energy absorbed in the loading-unloading cycle decreases. 3

4 The peak pressure is calculated as the average value across the heel surface. The values are significantly higher than in the human trials, while foam performance changes in far fewer impacts than in the human trials. Table 3 ASTM test results for the EVA foam midsole. session Impact number Maximum displacement (mm) Maximum pressure (kpa) Maximum force (kn) Energy absorbed (J) Figure 2 showed the force vs. deflection graphs for both sessions. The greatest shape change occurs in the first session, probably due to softening of the polymer part of the foam structure. The midsole response appears to approach an equilibrium response when impact number is high. The hysteresis in this response could in part be due to heat transfer from the compressed air in the cells to the cell walls. Fig. 2 Force versus deflection for the ASTM heel impacts on EVA foam midsole. STRESS ANALYSIS OF THE FOOT AND SHOE HEEL The ABAQUS FEA program (HKS) was used. Unpublished work showed that the response of EVA foam midsoles could be modelled in compression and tension using a single modulus version of the Ogden hyperfoam material. The problems tackled were axisymmetric, with a vertical axis of rotational symmetry. The large deformation option is used. Meshing was chosen to maximise the computation stability; nevertheless most simulations became unstable at high deformations. The geometry of the calcaneus bone of the heel is grossly simplified to be a hemisphere of radius 15 mm, attached to the end of a 20 mm long vertical cylinder of radius 15 mm. The heel pad is assumed to be bonded to the heelbone surface. This allows some of the load to be transferred by shear to the cylindrical surface. 4

5 The properties of the heel pad were adjusted until the force deflection response in problem (1) matched the data of Aerts et al (1995). Its outer geometry was a vertical cylinder of radius 30 mm and a flat end face, with a 10 mm radius to the edge. No account is taken of the confining effect of the shoe sides. The EVA midsole foam was taken as vertical cylinder of radius 35 mm and height 22 mm, with flat end faces. Three problems were considered: 1) The ASTM F1614 heel compressing an EVA foam midsole, resting on a flat rigid surface. The heel is a vertical steel cylinder, of 45 mm diameter and flat end, with a 1 mm radius to the edge. The Ogden hyperfoam data for the EVA foam were µ = 100 kpa, α = 0.5, Poisson s ratio = 0. 2) The deformation of the human heel pad in contact with a flat rigid surface. The heelpad was simulated using the Ogden hyperelastic material. The shear moduli were µ 1 = µ 2 = 200 kpa, the exponents α 1 = 2 and α 2 =-2, and the inverse bulk modulus D= 1.0 x 10-9 Pa -1. This is equivalent to the Mooney Rivlin equation for rubber, but with moduli typical of gels. Although the material model cannot simulate hysteresis on unloading, it can predict the shape of the mean of the loading and unloading curves. 3) The deformation of the heelpad, in contact with an EVA midsole, resting on a flat rigid surface, using the EVA foam parameters of the 1 st analysis and the heelpad parameters of the 2 nd analysis. Figure 3a and b show the vertical compressive stress σ 22 contours, respectively for the ASTM test and the heel/heelpad model at deformations of 11 and 17 mm respectively. 5

6 Fig 3 σ 22 stress distribution for a) ASTM heel on EVA midsole at 11 mm deflection b) Heelbone and pad on EVA midsole at 17 mm deflection. Contours in kpa. In the ASTM test, there is a sudden transition between nearly uniformly compressed foam under the heel and the surrounding foam. While the stress in the majority of the foam directly under the heel is in the range 250 to 300 kpa, it reaches a peak of 450 kpa at the heel edge. This is for a load of 0.55 kn, only 42% of the typical peak load in the ASTM experiments. Hence, the stresses would be higher if the simulation had reached the peak load of the experiment. In the heel plus midsole simulation, the upper midsole surface is concave, while the heelpad has spread laterally at a load of 0.70 kn. The maximum foam stress is 300 kpa, at the centre of the contact area on the foam upper surface (fig 3b). This is confirmed by the 240 kpa area of diameter approximately 20 mm in the Tekscan pressure map of the midsole upper surface. Peak footstrike forces (Nigg, 1990) are higher at 1.5 to 2 kn, but the FEA has ignored load transfer from other parts of the foot to the ground. The Tekscan pressure map, at the moment of maximum heelstrike, indicates that about 40% of the total force is transmitted through the heel region. The predicted force versus deflection relationships are shown in figure 4. With the deformable heel model, rather than the rigid ASTM heel, the deflection is 20% higher for a given compressive force. Hence a footstrike of a given kinetic energy will produce a lower peak force than in the ASTM test with the same kinetic energy. The predicted ASTM test force-deflection relationship has the same shape as, but is slightly lower than, the experimental unloading data (figure 2). Hence a better material model is required for the FEA of the loading response of EVA foam force kn ASTM Heel model deflection mm Fig 4 Force vs deflection for EVA midsole compressed with ASTM rigid heel and heel/heelpad. Gas loss modelling The loss of air from the EVA foam under creep loading was modelled using onedimensional finite difference methods (Mills and Perez, 2001). The air flow was along the direction of the compressive stress. The model predicts that a gas-depleted layer develops at the upper and lower surfaces of the foam. In rapid heelstrikes, a similar process should occur, but the timescale is difficult to predict. Applying these results in a qualitative manner to heelstrikes on EVA midsoles suggests that a gas 6

7 depleted layer should develop near the upper surface of the midsole, in the high pressure region indicated by the Tekscan results. DISCUSSION The ASTM test, used for shoe midsole testing, produces a different pressure distribution on the upper surface of an EVA midsole than either those recorded inshoe, or that predicted by FEA of the heelpad plus EVA foam. The peak forces in the ASTM test are too high, because it ignores forces transmitted through the rest of the shoe during heelstriker, producing excessive pressures on the foam. FEA indicates a high pressure region on the foam at the edge of the ASTM heel, which is quite different from the in-shoe measurements with runners, or the FEA prediction for a heel/heelpad model on a midsole. The ASTM test probably causes a more rapid deterioration in the midsole response than does running. Further FEA will be done of the effect of air-depleted foam in upper central region of the midsole. The modelling of gas loss from the foam under uniform-stress creep conditions indicates the process rate, and the development of a depleted gas region near the foam upper and lower surfaces. However when shoes are used for running a) The foam pressure distribution is non-uniform, with peak values near the centre of the heel contact area. b) The impacts, repeated at 0.3 s intervals, may cause fatigue damage to the foam. The above suggests that foam cell flattening should be seen near the upper surface of the midsole, near the heel centre. We will check the shoes after 500 km of use. The observations quoted by Bartlett (1985) may be wrong, as the process of moulding the midsole into its final form can cause the flattening of surface cells. The thin cell faces of EVA foam are not perfect for containing air. As the air provides a major shock cushioning mechanism in the foam, its loss reduces the midsole performance. There is a complex interaction between the heel-strike stress field in the foam and the gas diffusion from the foam. Although the gas diffusion can be modelled during uniform creep loading, it is not yet possible to consider all aspects of the stress-diffusion interaction. REFERENCES Aerts P. et al, (1995) J. Biomech. 28, Ahroni J. H. et al, (1998) Foot & Ankle Int., 19, Barlett R., (1995) Sports Biomechanics, Spon. Gefen A. et al, (2001) J. Biomech. 34, Misevich K.W. & Cavenagh K.W., (1984) Ch. 3 in Sports Shoes and Playing surfaces, Eds. EC. Frederick, Human Kinetics Inc. Mills N.J., (1994) Impact response, in Low density cellular plastics, Eds. Hilyard N.C. & Cunningham A., Chapman & Hall, London. Mills N.J. & Rodriguez-Perez M.A., (2001) Cell. Polym., 20, Nigg B., (1990) Ed. Biomechanics of running shoes, Shoe Trades Publ. Co., p 29. Thompson R.D. et al, (1999) Sports Engng. 2, ASTM F1614 Shock Attenuating Properties of Materials Systems for Athletic Footwear, American Society for Testing and Materials,