In-Class Case Study:
Determining the Mechanical
Properties of Bone
Using State-of-the-art Mechanical
Testing System (MTS Bionix)
Prepared by Prof. Deepak Vashishth
Biomedical Engineering Department
Rensselaer Polytechnic Institute
Permission is granted for non-commercial use
Specific Aims
• Demonstrate tensile testing of cortical bone.
• Analyze the test data to extract the mechanical
properties of the bone.
• Draw conclusions about
– the mechanical properties of bone
– limitations of linear elastic assumptions
• Use mechanical properties under tension,
compression and torsion to analyze fracture
surfaces of bone
In-Class Exercise
• Form the class into four groups of students
• Each group discusses and specifies one of the
following four steps necessary to the study.
–
–
–
–
1. The hypothesis for experimental investigation
2. The testing required to validate the hypothesis
3. The physical design of test specimens
4. The experiment protocol and data analysis
• The next four slides show issues to be considered
by each of the four groups.
Mechanical Properties of Cortical Bone
1. Possible Hypotheses
a. Bone is weaker in tension than in shear.
b. Bone is stronger in tension than in shear but:
Tensile yield stress < 2(Yield stress in shear)
c. Bone is stronger in compression than in tension.
d. Bone is stronger in compression than in shear.
e. Compressive yield stress > 2(Yield stress in shear)
Mechanical Properties of Cortical Bone
2. Required Testing
• Monotonic tests can determine the yield and
ultimate strength under tension, compression and
torsion.
• The properties vary with the rate at which
specimens are tested. – (Use a fixed rate.)
• The rate should be similar to in vivo rates – i.e.
rates at which the body loads the bone (Burr et al.,
1996).
Mechanical Properties of Cortical Bone
3. Design of test specimen
• First alternative: testing of whole bone
– Geometric variations occur in the bone and affect the
measured mechanical properties.
– The calculation of stress and strain is difficult if not
impossible due to these variations.
• Second alternative: testing of specimens machined
from whole bone, producing a standard geometry:
– Test results vary with material properties only.
– Fracture will be at a predictable site.
– Stress and strain can be easily calculated.
(continued)
Mechanical Properties of Cortical Bone
3. Design of test specimen
Typical Dimensions (in mm)
Reference: Vashishth et al., 2001
Y
X
20
24
10
6
20
3
5
Stress = Force/ [p*(0.003^2)/4]
Strain = (dL/10)
dL- measured via an
extensometer
Preparation of test specimen
Mechanical Properties of Cortical Bone
4. Experimental set-up & data analyses
See next slide for Lab image
and
Optional:
Use NetMeeting to connect on-line to the
Orthopaedic Biomechanics Laboratory
Department of Biomedical Engineering
Rensselaer Polytechnic Institute
MTS Testing Facility @ RPI
Pod Controller
Computer Interface
Specimen
Grips
Multi-axial Load Cell
MTS Signal Generator
Mechanical Properties of Cortical Bone
4. Experimental set-up & data analyses
• The next two slides show the user interface
screen display for the MTS during the
experiment.
• The notes that accompany each slide are
keyed to the numbers shown overlaying the
screen display.
MTS Software
4
1
3
5
Running the Test
See next slide for Lab image
And link to
A video file shows the fracture of the bovine
bone specimen
Optional:
Use a WebCAM to connect on-line
to the
Orthopaedic Biomechanics Laboratory
Keep eyes on
fracture site
V-Groove
Grips
Extensometer
Link:http://tc.bme.rpi.edu/MTS%20Package/DryBoneTensile.avi
Username: biomed
Password: guest
The data generated from this experiment
is compiled in an Excel file. Link to this
file to see data. There will be two sheets
on this file. The first sheet will be the raw
data and the second will be the calculated
data.
Link to wet bone tensile test Excel file
Username: biomed
Password: guest
The MTS Test Results
Biomechanical Testing of Bone
180
Stress (MPa)
160
140
Wet Bone
120
100
80
60
40
20
0
0
0.01
0.02
Strain
0.03
0.04
Critical Points on a generalized stressstrain curve
Determining the Yield Stress (Y)
using 2% offset
MTS Test Results
Mechanical Properties of Cortical Bone
E (0.1-0.3%)
=23.45 GPa
Yield Point Calculation
Bone Tensile.xls
200
Stress (MPa)
150
100
Ystress = 135 MPa
Ysrain = 0.0077
50
0
0
0.01
0.02
-50
Strain
0.03
0.04
MTS Test Results
Mechanical Properties of Cortical Bone
Modulus vs Strain (Tensile Test)
Is the assumption
of linearity valid?
30
Modulus (GPa)
25
20
0.2% offset – Is
it justified?
Yield Point
15
10
Bone Tensile.xls
5
0
0
0.005
0.01
0.015
Strain
0.02
0.025
0.03
Case Study Wrap-up
• The results of experimental analysis for a
large number of bone tests are shown in the
next slide.
• We will look again at our initial hypotheses
and draw conclusions based on the results.
• For homework, we will see if the results
from the in-class case study appear similar
to the large sample results.
Material Properties of Cortical Bone (Vashishth 1997)
Loading
E
G
Ystrain Ystress U.Strain U.Stress
(GPa) (GPa) (%)
(MPa)
(%)
(MPa)
Tension
22.9
(2.2)
0.80
(0.03)
131
(5)
3.89
(0.79)
159
(8)
Compression
22.4
(2.5)
1.19
(0.11)
207
(23)
1.22
(0.16)
210
(22)
1.39
(0.24)
68
(7)
2.0
(0.15)
84
(11)
Torsion
5.6
(0.8)
Hypotheses
Biomechanical Testing of Cortical Bone
Looking again at each possible hypothesis, we can accept
or reject as follows:
1:Bone is weaker in tension than in shear
2:Bone is stronger in tension than in shear but:
Tensile yield stress < 2(Yield stress in shear)
3: Bone is stronger in compression than in tension.
4: Bone is stronger in compression than in shear.
5:Compressive yield stress > 2(Yield stress in shear)
Homework Exercise
• Using the data file generated from the dry bone
tensile experiment, calculate:
– Elastic Modulus
– Yield stress and strain
– Ultimate stress and strain
• Compare the differences between the wet bone
experiment and dry bone experiment.
• Using the yield strength values obtained under
tension, compression and shear, explain the failure
of bone under tension and compression*.
Username: biomed
Link to Dry Bone Tensile Test File
Password: guest