Performance of EVA foam in running shoes

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Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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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 rapid-
compression 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

Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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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/m3 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 82.2 56.7 19.8
Grey 82.0 53.6 18.7
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 brand-
new 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.

Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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Table 2 Peak pressures values (kPa) for the runners
session first second
runner 1 min
5 min
10 min
Distance
Run (km) 1 min
5 min
10 min
1 280 301 311 106.2 286 321 342
2 245 262 273 30.9 250 283 310
3 232 259 275 52.3 240 279 306
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 26th 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.

Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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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)
1 1 7.31 764 1.21 3.28
1 26 7.74 817 1.30 2.58
2 1 7.57 799 1.27 2.91
2 25 7.73 817 1.29 2.60
2 50 7.76 863 1.37 2.17
2 75 8.03 787 1.25 2.80
2 100 7.79 872 1.39 1.93
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.

Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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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 µ1 = µ2 = 200 kPa, the exponents α1= 2 and α2=-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 1st analysis and
the heelpad parameters of the 2nd analysis.
Figure 3a and b show the vertical compressive stress σ22 contours, respectively for the
ASTM test and the heel/heelpad model at deformations of 11 and 17 mm respectively.

Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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Fig 3 σ22 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.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12 14 16
force kN
deflection mm
ASTM
Heel model
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 one-
dimensional 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

Pp 580-587, The Engineering of Sport 4, Eds S. Ujihashi and S.J. Haake, Blackwell (2002).
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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 in-
shoe, 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, 1299-1304.
Ahroni J. H. et al, (1998) Foot & Ankle Int., 19, 668- 673.
Barlett R., (1995) Sports Biomechanics, Spon.
Gefen A. et al, (2001) J. Biomech. 34, 1661-1665.
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, 79-100.
Nigg B., (1990) Ed. Biomechanics of running shoes, Shoe Trades Publ. Co., p 29.
Thompson R.D. et al, (1999) Sports Engng. 2, 109-120.
ASTM F1614 Shock Attenuating Properties of Materials Systems for Athletic
Footwear, American Society for Testing and Materials, 1999.