Effects of Heel Height on Stress
Distributions in Bones of the Feet
Vanvisa Attaset
EN 175
Professor Blume
6 December 2001
Motivation
“Ladies
who must wear certain fashionable boots should, as a preliminary
measure, have the three middle toes amputated. The operation would add to their
comfort, would render their gait not one whit more awkward than it is at
present, and would be but a very little less sensible than the Chinese practice
of deforming the feet in infancy”
F. Treves, 1884
Physicians have a historical battle
with the practice of wearing high-heeled shoes. These shoes have been proven
time and time again to concentrate forces in sensitive areas of the feet,
deleteriously affect musculature and energy output, and lead to chronic
disorders. However, these warnings go unheeded as millions of women continue to
be more greatly influenced by current fashion trends. Especially as more women
join the workforce, high heels are being worn for extended periods of time. As
taller heel heights become more popular for extended wear, I wanted to examine
the effects of different heel heights and see where the stress concentrations
occur in order to understand the foot pain that often accompanies the use of
high heel shoes. In addition, by studying several heel heights, perhaps a
“safe” heel height can be determined for women who must wear these types of
shoes.
Goals
First, I had decided that I wanted
to compare stresses in a foot of a person who is standing in shoes of different
heel heights. I decided to model a foot in heels of 3, 6, and 10 centimeters in
addition to the foot that would be modeled as simply flat. I was especially
interested in the compression of the bone at the front of the foot, around the
toes. In addition to comparing the results of the different heel heights, I
decided that I wanted to be able to compare feet in the same heel in different
situations. I chose to model the foot with the ankle at an angle to simulate
leaning, or perhaps a moment while walking. I could then compare the stress
concentrations at different heel heights in this situation as well as comparing
the results to the standing results.
Modeling
1.
Drawing and Materials
Before any modeling could be done,
the bone anatomy of the foot needed to be understood. Since the entire foot
would be complicated to model due to the many interactions and various
materials, it was decided that modeling the bones would be an adequate start.
Figure 1 shows the bone structure of the foot. Partly based on the complexity
of this structure, a 3-D model was disregarded. In addition, it was assumed
that the stresses would be somewhat constant over the width of the foot so that
a 3-D model was not necessary and if a simplified 3-D model had been attempted,
the results in the areas of interest, particularly the toes, would likely be
inaccurate due to the necessary idealizations.
Approximate cut for 2-D profile
Figure
1
A two-dimensional model was decided upon, the profile
being that of a vertical cut from toes to heel around the middle of the foot
width. Additional simplifications were made to handle the multiple bones of the
foot. The cross section was idealized as containing four main bones. In
reality, each of these large bone sections if composed of many smaller bones.
The four large bones in the model were separated by thin sections of a
different material in order to simulate joints. There was also a thin pad of
similar material placed along the bottom of the foot to act as the pad of skin.
The foot in a standing position was
modeled with a vertical anklebone so that the load could be applied straight
down. Another model was made that changed the angle of the anklebone in order
to apply a pressure from a different direction. These models were drawn for the
flat foot and the 3, 6, and 10 cm heeled feet.
Bone Pad Joints
Figure 2. Profiles of flat standing foot (left) and angled foot (right) with sections labeled
The
total length of the surfaces on the bottom of the foot is 23 cm and this was
kept constant throughout all the models. The diameter of the anklebone is 4cm.
The thickness of the bottom pad is 13 mm. The material properties of each of
the sections are given in the table below.
|
|
Bone |
Joints |
Pad |
|
Young’s modulus |
16 GPa |
4 GPa |
4 GPa |
|
Poisson’s ratio |
0.3 |
0.4 |
0.38 |
.
2. Boundary Conditions and Loads
Both the standing and the angled
situations were modeled to be static. All of the models had boundary conditions
of U2 = 0 on the bottom front and bottom heel surfaces. The small surface at
the toe was bound to U1 = 0. For the flat and 3 cm heeled models, U2 = 0 also
at the middle surface on the bottom of the foot. However, when the foot became
more angled as the heel height increased, that condition did not seem very
plausible. Therefore, the 6 and 10 cm heeled models have a boundary condition
on the bottom middle surface so that they are constrained in the direction
normal to the surface.
All of the models are loaded with a
pressure of 15900 N/m2 as determined by a 25 kg woman putting half
her weight on the cross-sectional area of one ankle.
Load:
15900 N/m2 BC:
U1=0
BC:
U2=0 BC:
U2=0 or U=0 in normal direction
Figure 3. Boundary conditions and loads on model
3.
Analyses
The models were all meshed using a tri-element. A quad-element was
attempted, but it could not mesh the thin pad on the bottom. The approximate
element size is 30 mm. Then, for each heel height, a job was performed with the
specified pressure for both the vertical and the angled anklebone models.
Various components of stress were then analyzed and compared among the
different models.
Results
and Discussion
Before the analyses were run, it was
assumed that the compressional forces in the foot were going to be of the
greatest interest. Contour plots of minimum in-plane principal stress allowed
the compression in the cross-section to be studied and quantified (Figures
4-7). A graph of the minimum minimum in-plane principal stress (greatest
compression) shows that it compresses more as the heel height increases and
there is greater compression when the ankle is angled, such as when walking
(Chart 1).
