I.
Experimental Techniques for Shoe Sole Material Selection
1.1
Foot Protection
In order to test materials for their ability to protect the foot, a puncture test can be used. A puncture
test gages the ability of a material to withstand puncture from a sharp object, such as a rock or a nail that might
be encountered on a daily basis while walking/running. In order to perform a puncture test, one must cut out
rectangular samples of the material to be tested. Using a uniaxial tension/compression apparatus, with a
puncture fitting, one can measure the amount of force necessary to puncture the material.
Additionally, the hardness test can be used to measure the amount of deformation that takes place due
to an indentation at a certain force. This test can be performed in two ways: using a hand-held durometer or
using a Rockwell Hardness Machine. In our particular lab, we used a durometer, which returned a number
correlating to the hardness of the material being tested. Lower numbers correspond to softer materials,
whereas higher numbers correspond to harder materials.
1.2
Permitting for Motion while Offering Stability
When selecting materials that permit motion, it is optimal to choose materials that have the ability to
substantially deform while keeping their initial shape. By using a tension test, it is possible to calculate the
Young’s Modulus (E) and Yield Strength (  f ) of each material. In preparing this experiment, a tensile testing
apparatus is used. Specimens are shaped like an hour-glass, and cut out of a sheet of raw material using
hourglass-shaped male and female cutters placed in a tensile testing device. These specimens are clamped into
the tensile testing apparatus (with the fat ends of the hourglass clamped so that deformation takes place in the
skinny neck of the specimen), and a steadily-increasing load is applied until the specimen ultimately fails.
Values for Load vs. Displacement are uploaded into an excel file.
In testing for stability, the creep component becomes important. In a shoe, it is necessary that the shoe
be able to deform significantly and experience very little plastic creep over time. In light of this, a
compression/creep test can be performed. Specimens are cut out of circular-shaped dies with a very tiny (~5
mm) radius, and placed in a tensile testing apparatus. Lubrication is used so that the specimen doesn’t
experience surface shear forces due to the friction between the specimen and the flat clamps that will be
compressing it. A steadily-increasing load is applied until the specimen undergoes a certain strain, after which
the load remains constant. Creep is measured by analyzing the data in the form of an Engineering Strain vs.
Time graph.
1.3
To Store and Release Energy
While measuring the ability of a material to store and release energy, it is adequate to simplify the
energy-storage capabilities of a material to that of an axial or leaf spring. With this spring simplification in
mind, we can use the data obtained from a tension and a cyclic test. The experimental setup for a tension test
was described in Section 1.2. The cyclic test is similar to the compression test discussed in Section 1.2, but
instead, the material is taken through a cycle of loading conditions where the strain remains linear throughout
the whole cycle. Data is uploaded in the form of force vs. displacement into an excel file.
1
1.4
To Dissipate and Absorb Energy Upon Impact
To measure a material’s ability to dissipate and absorb energy, tension tests and cyclic tests can be
performed in order to derive the Young’s Modulus and fracture strength. The experimental setups for both of
these tests are described in Section 1.3.
II.
Energy Storage/Dissipation in Elastomers
As explained in Section 1, tensile testing is the best way to measure energy storage in a material. By
using date recorded from the lab, we can compare and contrast the energy storage capabilities of natural rubber
and polyurethane. According to the data recorded from these tensile tests, Polyurethane recorded a Young’s
Modulus of around 23.4 MPa, whereas Natural Rubber recorded a Young’s Modulus of ~1 MPa. A graph of the
cyclic loading results for both of these materials is available in Figure A-1 of the appendices. As is evident from
the graph, the polyurethane deformed a lot less given a certain amount of stress. Additionally, throughout the
course of the cycle, the material “crept” a little bit, as it did not follow the same slope back to zero strain each
time.
The discrepancies noted in Figure A-1 can be traced back to the microstructural components of each
material. In the case of polyurethane, a phase separation occurs between hard and soft copolymer chains. As
the material is deformed, the soft chains uncoil and the hard chains re-orient themselves in the direction of
stress, thus increasing the overall fracture strength but making the material less prone to deformation. On the
other hand, natural rubber consists of long polymer chains that are sparsely interlinked, giving rubber greater
flexibility but decreasing the fracture strength.
III.
Selecting Materials for Various Desirable Characteristics
a.
b.
c.
Polyurethane and Leather had the highest puncture resistances and greater durometer readings,
according to Figures A-2 and A-3 in the appendices. It may be noticeable that cardboard and
neoprene recorded a higher durometer reading than leather, but both of these materials recorded
very tiny puncture resistances and therefore are not suitable candidates. The comparative results
for hardness and puncture resistance are available in Table T-1.
Natural Rubber and EPDM 60 had least amount of creep. This conclusion was drawn from close
inspection of Figure A-4, which displays engineering strain vs. time for various materials as
recorded from the creep tests. According to this graph, Natural Rubber and EPDM 60 experienced
the most constant strains after the critical point where force was held constant, and therefore had
the least amount of creep.
Energy storage is maximized when the curvature of a material in the case of an elastic hinge is
maximized. This is because the hinge acts as a spring, and the spring stores a greater amount of
potential energy when the radius of curvature is the smallest (or the curvature is highest). This
ffffffff
f
. According to Table T-2, the appropriate
E
selections for energy storage are Neoprene Foam and Natural Rubber
condition is characterized by the material index of
d.
In choosing materials for absorption and dissipation of energy as an elastic hinge, two properties
2
ffffffff
f
become important: E and  f . The material index for this property is
, and this index for various
E
materials is presented in Table T-2. As is evident from the table, Polyurethane and Neoprene are
the best choices for storing and releasing energy.
2
The results given above are summarized in Tables T-1 and T-2 shown below.
Material
Natural Rubber
Polyurethane
Leather
Foam Rubber
Cork
Neoprene Foam
Neoprene Spring Rubber
Buna-N
EPDM 60
F Puncture [N]
25
193
294
NA
51
24
NA
72
78
Ranking
6
2
1
H Durometer
Ranking
7
1
2
9
6
8
3
5
4
41
98
76
17
51
25
73
60
69
5
7
4
3
Table T-1: Puncture Load and Hardness Comparisons for Materials
Material
Natural Rubber
Neoprene Foam
EPDM 60
Neoprene
Polyurethane
Buna-N
E
[MPA]
1
.23
1.9
4.2
23.4
2.8
f
Ranking
Ranking
[MPa]
.57
.17
.97
1.5
7.7
.77
ffffffff
f
E
5
6
3
2
1
4
.56
.73
.50
.36
.33
.27
2
1
3
4
5
6
2
ffffffff
f
E
.32
.12
.48
.54
2.5
.21
Ranking
4
6
3
2
1
5
Table T-2: Strength and Material Indices Comparisons for Elastomers
IV.
Energy Tradeoffs
As is evident from the comparative results given in Table T-2, the ability to absorb energy is often
inversely proportional to the ability to store energy for a given material. Therefore, if one were to select a
single material for both of these purposes, one would have to settle for a material such as EPDM 60, which is
average in both energy storage and dissipation.
In order to counter this debacle, it is possible to combine materials. In the case of a shoe, we can choose
a material with high energy dissipation to be on the inner-surface that contacts the foot, so that the foot
experiences the most comfort when impacting a rough surface. We can then choose the material with high
energy storage for the bottom of the shoe, so that the sole can store and release the energy provided by the
ground impact, thus making it easier to “propel forward” in a spring-like fashion when the shoe leaves the
ground.
V.
Material Indices
We have chosen to select a shoe layout as depicted in Figure T-3, shown below.
3
Figure T-3: Layered Structure for Shoe Sole Design
5.1
Material A
For the section denoted by Material A, energy absorption and creep are the important constraints.
Therefore, we want to choose a material with the following conditions:

Maximize curvature, energy dissipation upon impact ( M 1 

Minimize creep to provide adequate stability
5.2
ffffffff
f
)
E
Material B
Material B is in direct contact with the ground, so puncture resistance and hardness are the most
important conditions to design around. Additionally, it must be able to store and release energy effectively.
Therefore, the following conditions are pivotal:
 Maximize fracture strength  f ( M 2   f )

5.3
2
ffffffff
f
Maximize energy storage and release following impact ( M 3 
)
E
Material C
Material C is exposed to external forces, so puncture resistance and hardness are important.
Additionally, Material C is responsible for the “springiness” of the shoe, which is the ability of the shoe to
recoil and propel the wearer forward after ground impact. Thus, energy storage and release is important.
Conclusively, the material C should be selected according to the following parameters:
 Maximize fracture strength  f ( M 2   f )

5.4
Maximize energy storage and release following impact ( M 3 
Appropriate Material Groups for Selected Indices




Creep: Non-Elastomers
f
M 1  ffffffff: Elastomers
E
M 2   f : Metals
2
ffffffff
f
M 3  : Elastomers
E
4
2
ffffffff
f
)
E
VI.
Final Selection
Material A: Natural Rubber
Natural Rubber is the best choice for Material A. Referring back to Table T-2, Neoprene Foam and Natural
Rubber were the front-runners in energy dissipation. However, because Natural Rubber experiences
significantly less creep in Figure A-4, it is the best candidate.
Material B: Polyurethane or Leather
Polyurethane is the best selection for Material B. In Table T-2, it has the highest  f as well as the greatest
amount of energy storage according to M 3 
2
ffffffff
f
. Leather is also a contender because it is by far the most
E
puncture-resistant.
Material C: Polyurethane
Polyurethane is the best choice for material C, since energy storage is the most critical condition to design
around in this case. This is evident by inspecting Table T-2.
The following are some material considerations that were not taken into account:
 Shear forces (friction between ground and shoe)
 Chemical Reactions
 Weight, Volume, Density
 Price, availability of materials
 Thermal expansion
 Fatigue, resistance to long-term wear and crack propagation
 Fracture toughness
5
VII.
Appendices
Figure A-1: Engineering Stress vs. Engineering Strain for Natural Rubber
And Polyurethane
Material
neoprene rubber
natural rubber
polyurethane
leather
foam rubber
cork
neoprene foam
neoprene spring
rubber
cardboard
buna-N
EPDM
Reading
80
41
98
76
17
51
25
73
89
60
69
Figure A-2: Durometer Readings for Various Materials
Material
6
force(N)
neoprene rubber
natural rubber
polyurethane
leather
foam rubber
cork
neoprene foam
neoprene spring rubber
cardboard
buna-N
EPDM
NA
25
193
294
51
24
NA
NA
72
78
Figure A-3: Puncture Forces for Various Materials
Figure A-4: Creep Comparison for Various Elastomers
7