Contact Mechanics of Prosthetic Hip Joints
Submitted as a Final Project in Friction, Lubrication and Wear of Materials
By Dan Flavin
RPI Hartford, Fall 2013
INTRODUCTION:
As the human population ages, an increasing number of senior citizens will find themselves
with replacement body parts. These may include artificial hips and knees, two of the most common
prosthetic implants in modern medical practice. Joint replacement surgery is used to treat the
effects of a wide variety of illness and injuries, including arthritis, various forms of tumor, or
traumatic injury. However, current medical implants often have a limited lifespan, requiring
multiple surgeries to upgrade the internal hardware as the implant and patient age.
Two of the most common joint replacements are the hip and the knee. In order to simplify
the analysis due to limited computing power, the joint chosen for modeling was the hip joint. In the
human hip, the head of the femur (thigh bone) is a globular protrusion extending off the upper and
inner portion of the femur. This nearly spherical protrusion seats into the acetabulum, or cotyloid
cavity, a concave portion at the base of the pelvis, allowing a broad range of motion for the hip
joint. In essence, the hip joints acts as a ball and socket joint, which can be much more easily
modeled than the complex compound curves of the lower femur knee joint.
Modern hip implants consist of two parts: the acetabular cup, and the femoral prosthetic.
The acetabular cup is implanted into the pelvis, and may be formed of one or two pieces
(monobloc or modular, respectively). The femoral prosthetic is mounted atop the femur, and may
also be monolithic or modular. While a variety of techniques have been developed to mount the
various models of prosthetic in the patient, they are outside the scope of this study.
In looking at the history of the artificial hip, the early major milestone was the
establishment of the Metal-on-Polymer (MOP) implant in the late 1960s, which became the
standard implant by the early 1970s. This implant has a stainless steel (almost universally 316L)
monobloc femur implant, with a head of around 22mm diameter, and a modular polymer
acetabular cup. The acetabular cup usually had a stainless shell on it to help bond to the pelvic
bone, and, originally, a Teflon polymer component. However, early failure of the Teflon cups after
only a few years lead to its replacement with ultra-high molecular weight polyethylene
(UHMWPE). An example of this type of hip prosthesis is show in the figure below.
Fig 1. - MOP Style Replacement Hip (from manufacturer’s
website)
These implants were common and for the most part worked fairly well, though wear on the
polymer cup could lead to polymer debris entering the tissue surrounding the joint, causing paint to
some patients after ten to twelve years. In an effort the address this issue, two other styles of
implant were developed during the 1990s and early 2000s.
The first of these was the Metal on Metal (MOM) implant, where both surfaces were either
stainless steel or cobalt-chromium (CoCr) steel. Some of these implants used a larger femur head
and thinner acetabular cup, allowing better joint stability and reducing dislocations at the expense
of higher friction loads and increase inertia loads on the tissue.
The second approach was to form various parts of, or coat them with, ceramic materials.
This included Ceramic on Ceramic (COC) implants where both head and cup are lined with
ceramic material, or Ceramic on Polymer (COP) implants, where a ceramic head seated in a
polymer cup. The harder, more polished surface of the ceramic is claimed to wear less on the liner
of the cup, increasing the lifespan of the implant.
While these were marketed as a substantial advance on the older MOP implants, studies
have yet to demonstrate a significant increase in lifespan of the MOM and COC implants, and
several notable drawbacks have surfaced. In rare occasions, the ceramic components of the COC
or COP implants can fracture or chip after implantation, leading to accelerated failure of the
prosthetic. MOM implants can shed sufficient debris to cause bone and tissue damage, which has
been a sufficiently widespread issue to force at least one recall and a number of medical groups
encouraging a ban on several models.
THEORY AND METHODOLOGY:
The continued issues with prosthetic hips have led to a closer examination of wear for
many of the material combinations medically available. Much of this research has been done
empirically, through extensive laboratory testing in both academic and commercial fields.
However, attempts have also been made to model the various conditions mathematically, in order
to gain a better understanding of the variables involved. The human body is a complex mechanism,
and the variable lubrication properties of synovial fluid (a non-Newtonian, thixotropic fluid found
in human joints) have created a number of problems for researchers.
However, one of the basic questions of contact area, which seems it would be relatively
simple to calculate, has proven complicated as well. The clearance between the head of the femur
implant and the acetabular cup can vary by both design and manufacturing tolerance, and the
curvature of both the head and the cup complicate Hertzian analysis of the system. While several
mathematical methods have been attempted to model the contact mechanics of the joint, they have
reached limited accuracy. Numerical methods have also been used, and this study is intended to
develop a relatively simple finite element analysis (FEA) approach using the COMSOL software
to the question of contact area. If the model proves reliable, it can be further refined to potentially
assist in analysis of the wear conditions within that contact area.
The variables which the model needs to encompass include: the radius of the femoral
implant head, the clearance between the femoral head and the acetabular cup, and the material for
both parts of the joint. Loading will be held constant at 2500 N, a number commonly used in the
available literature as being roughly three times the body weight of an average adult. The thickness
of the acetabular cup will also be held constant at 20 mm, though in the case of unlined metal cups
this is above the actual thickness. Both load and thickness are easily changed in the model,
however, if these values prove unreasonable for a specific situation.
The model itself is built with divisions for the use of COC liners, which are generally
4-6mm thick on the cup. The femur head of a COC prosthetic may have a similarly thick liner, or
may be a solid piece of ceramic. In the model, both are modeled at 5mm thick. Note that the shell
of the liner is not modeled here, as it will have minimum influence on contact forces. This model
uses alumina ceramics, which are one of several available for the purpose. However, many
manufacturers use proprietary ceramic formulations with unpublished mechanical properties.
Alumina (aluminum(III) oxide) is a well-known industrial ceramic, and has well established
mechanical properties.
The model, as shown in Fig. 2, is built in COMSOL on a 2D axisymmetric model. The
inner femoral head contacts the inner edge of the acetabular cup only at the maximum Z value of
the head arc, with the space between them increasing to the maximum clearance gap at the lowest
point of the joint surfaces. If these two surfaces start out of contact, the model fails.
Fig. 2 - Model Geometry, with parts labeled
(this is a 16mm radius head with a 100µm clearance)
Once the geometry is built, the outer edge of the acetabular cup is restricted from motion.
The lower boundary of the femoral head is loaded with a distributed load with a total value of
2500N in the positive Z direction.
The following values were established from published literatures and used for variables in this
system of models:
Variable
Acetabular Cup Thickness (mm)
Femoral Head Radius (mm)
Joint clearance (µm)
Load (N)
Value(s)
20
11, 16, 25
50, 100, 150
2500
Three material combinations were considered:
 Metal on Metal (MOM), with a 316L stainless steel for both head and cup
 Metal on Polymer (MOP), with a CoCr steel head and a UHMWPE cup

Ceramic on Ceramic (COC), with alumina being used for head and cup liners, with the
remainder being titanium
The table below shows the mechanical properties of the materials used:
Material
316L Stainless Steel
CoCr Steel
Ti-6Al-4V
UHMWPE
Alumina
Modulus of Elasticity (GPa)
210
230
114
1
380
Poisson’s Ratio
0.3
0.3
0.3
0.4
0.3
Density (kg/m3)
7850
9200
4500
930
3960
Each combination of materials was modeled with each head size and clearance
combination. This
resulted in a total of 27
models. Meshing of each
model was done using
the “Extra Fine” setting
on the automatic, physics
drive mesh. A standard
mesh for the geometry
show in Fig. 2 is
demonstrated below in
Fig. 3. Efforts to refine
this mesh around the area
of initial contact met
with limited results, due
to limited computing
power. Increasing the
mesh greatly increased
the run time to upwards
of 30 minutes, yet
resulted in a failure to
Fig. 3 – Standard meshing (loaded surface is highlighted blue)
converge despite
increases in iteration limits to over 1000 iterations. Further discussion of this issue is found in the
Results and Discussion section.
For each model, once run, a calculation of the resulting contact arc between the head and
the cup was done by integrating a Boolean where the contact distance was less than 1 x 10-12
meters. This value was chosen due to the slightly imprecise nature of FEA; when the Boolean
value was the gap equals zero, small variations in calculation resulted in irregular results. This arc
length was used to calculate a contact area, which was based on the assumption that despite the
loading, the femoral head was still very nearly spherical.
RESULTS AND DISCUSSION
A table of raw data is available in Appendix A. The resulting chart of contact areas is
shown in Fig. 4, below.
Contact Area by Material Combination and Head
Radius
0.02
COC (11mm)
0.015
Area (m^2)
MOM (11m)
MOP (11mm)
COC (16mm)
0.01
MOM (16mm)
MOP (16mm)
COC (25mm)
MOM (25mm)
0.005
MOP (25mm)
0
5.00E-05
7.00E-05
9.00E-05
1.10E-04
1.30E-04
1.50E-04
Joint Clearance
Fig 4 – Contact Areas, charted by material type and femoral head size
As might be expected, the contact areas for the COC and MOM materials the contact area
decreases as the joint clearance increases, and goes up with the increasing head size. The MOP
contacts are much larger, and more varied as well. A deeper look at the results gives the suggestion
that further refinement in required before this model may be considered valid for the MOP design.
Examining the individual charts of Fig 5, which show the percentage of the hemispherical femoral
head in contact with the acetabular cup, shows that the values for MOM and COC joints act more
or less as expected; larger heads and larger clearances both result in a decreased percentage of the
head in contact. However, the MOP joint chart in 5C shows widely varying values, particularly for
the intermediate clearance value (100µm). Looking at the images of the calculation result for the
16mm radius head, 100µm clearance for each combination, as shown in Fig 6, shows expected
results for MOM and COC, and similarly anomalous results for the MOP model.
MOM Surface Area Use
(by joint clearance, in µm)
MOM (50)
MOM (100)
MOM (150)
Contact Percent
4.00%
3.00%
2.00%
1.00%
0.00%
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
0.026
Head Diameter
Fig 5A - Percentage of the Femoral Head in Contact with the Acetabular Cup in MOM Joint
COC Surface Area Use
(by joint clearance, in µm)
Contact Percent
COC (50)
COC (100)
COC (150)
2.50%
2.00%
1.50%
1.00%
0.50%
0.00%
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
Head Diameter
Fig 5B - Percentage of the Femoral Head in Contact with the Acetabular Cup in COC Joint
0.026
MOP Surface Area Use
(by joint clearance, in µm)
MOP (50)
MOP (100)
MOP (150)
35.00%
Contact Percent
30.00%
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
0.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
0.026
Head Diameter
Fig 5C - Percentage of the Femoral Head in Contact with the Acetabular Cup in MOP Joint
Fig 6A – MOM Joint COMSOL results
Fig 6B – COC Joint Comsol results
Fig 6C – MOP Joint Comsol Results
While Figs 6A and 6B show the expected high pressure contact point across the joint, Fig
6C shows a clear indication of questionable results as the low stress band in the femoral head
immediately opposite a high stress portion of the acetabular cup at the top of the joint. This
behavior was consistent across the MOP models to varying degrees, regardless of mesh size.
Increasing the mesh density beyond the point shown, however, resulted in a failure to converge
within 1200 iterations. Further confirmation of the oddity of this model are shown when going
back and plotting the gap between the contact pairs, as shown in Fig 7 along with the same plot
from the MOM model. Note the positive portion of the contact gap chart, near the origin, for the
MOP plot, as well as the step portion when it does go above zero. This is in contract to the smooth
plot for the MOM joint.
Fig 7A – Contact Gap Plot for MOP Joint
Fig 7B – Contact Gap Plot for MOM Joint
Further attempts to stabilize the MOP models may focus on refining the mesh at the contact
point, and reviewing the total displacement of the system under loading. It is possible that, despite
never entering the plastic zone of the materials, there is sufficient movement in the model under
loading that the large displacement plugin for COMSOL (not currently available at RPI) would
allow this model to operate properly. Other options would include load stepping, to gradually
increase the contact area and force a complete recalculation of stresses at each step of the increase.
CONCLUSION
The immediate results from the model suggest that while it does appear to function
properly for some models, others require further modification to give results that can be relied
upon. The models which used high Young’s Modulus material on both sides acted much as
expected. It was not until substantially different materials were introduced that the model begins to
break down.
The data from the valid models, however, could be refined and used for further wear and
friction testing. A wear vs. load plot for the various material combinations under both dry and with
synovial fluid (not currently present in available literature) would allow a better understanding of
the wear processes currently causing issues in patients, and combined with this model would allow
modifications of the design to minimize wear.
BIBLIOGRAPHY
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joint replacement: Current concepts in mechanical simulation." Medical Engineering &
Physics 30 (2008) 1305–1317
Askari, Ehsan. Flores, Paulo. Dabirrahmani, Dane. Appleyard, Richard. "Study of the
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Head material
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
CRES
CRES
CRES
CRES
CRES
CRES
CRES
CRES
CRES
CoCr
CoCr
CoCr
CoCr
CoCr
CoCr
CoCr
CoCr
CoCr
Cup material
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
Alumina
CRES
CRES
CRES
CRES
CRES
CRES
CRES
CRES
CRES
UHMWPE
UHMWPE
UHMWPE
UHMWPE
UHMWPE
UHMWPE
UHMWPE
UHMWPE
UHMWPE
Type
COC
COC
COC
COC
COC
COC
COC
COC
COC
MOM
MOM
MOM
MOM
MOM
MOM
MOM
MOM
MOM
MOP
MOP
MOP
MOP
MOP
MOP
MOP
MOP
MOP
APPENDIX A: Models and Values
Head radius
Clearance Peak vonMises Radius of
contact area average
(m)
(m)
(Pa)
Contact (m)
(m^2)
pressure (Pa)
0.011 5.00E-05
1.35E+08
0.00238
1.773E-05
1.410E+08
0.016 5.00E-05
8.71E+07
0.00307
2.952E-05
8.469E+07
0.025 5.00E-05
5.49E+07
0.00444
6.177E-05
4.047E+07
0.011 1.00E-04
3.09E+08
0.00202
1.278E-05
1.956E+08
0.016 1.00E-04
1.66E+08
0.00235
1.732E-05
1.444E+08
0.025 1.00E-04
1.11E+08
0.00379
4.504E-05
5.551E+07
0.011 1.50E-04
3.29E+08
0.00167
8.745E-06
2.859E+08
0.016 1.50E-04
2.90E+08
0.00235
1.732E-05
1.444E+08
0.025 1.50E-04
1.13E+08
0.0029
2.639E-05
9.473E+07
0.011 5.00E-05
9.82E+07
0.00264
2.179E-05
1.147E+08
0.016 5.00E-05
7.47E+07
0.00359
4.032E-05
6.200E+07
0.025 5.00E-05
3.97E+07
0.00508
8.079E-05
3.094E+07
0.011 1.00E-04
1.59E+08
0.00202
1.278E-05
1.956E+08
0.016 1.00E-04
1.29E+08
0.00307
2.952E-05
8.469E+07
0.025 1.00E-04
5.65E+07
0.00379
4.504E-05
5.551E+07
0.011 1.50E-04
2.91E+08
0.00202
1.278E-05
1.956E+08
0.016 1.50E-04
1.56E+08
0.00235
1.732E-05
1.444E+08
0.025 1.50E-04
9.92E+07
0.00379
4.504E-05
5.551E+07
0.011 5.00E-05
1.43E+07
0.00743
1.669E-04
1.498E+07
0.016 5.00E-05
7.72E+06
0.00359
4.032E-05
6.200E+07
0.025 5.00E-05
3.40E+06
0.02068
1.269E-03
1.971E+06
0.011 1.00E-04
1.68E+07
0.00681
4.515E-05
5.537E+07
0.016 1.00E-04
9.13E+06
0.00431
5.801E-05
4.310E+07
0.025 1.00E-04
3.94E+06
0.01452
6.439E-04
3.882E+06
0.011 1.50E-04
1.74E+07
0.00744
1.674E-04
1.494E+07
0.016 1.50E-04
9.47E+06
0.0079
1.921E-04
1.301E+07
0.025 1.50E-04
4.46E+06
0.01273
4.982E-04
5.018E+06