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 Bone1. 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
53
10 620 20
X
Y
24
Stress = Force/ [*(0.003^2)/4]
Strain = (L/10) L- measured via anextensometer
Typical Dimensions (in mm)
Reference: Vashishth et al., 2001
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 theOrthopaedic Biomechanics LaboratoryDepartment of Biomedical Engineering
Rensselaer Polytechnic Institute
MTS Testing Facility @ RPI
Specimen Grips
Pod Controller
MTS Signal GeneratorMulti-axial Load Cell
Computer Interface
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.
12
4
3
5
MTS Software
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 theOrthopaedic Biomechanics Laboratory
Extensometer
V-Groove Grips
Keep eyes on fracture site
Link:http://tc.bme.rpi.edu/MTS%20Package/DryBoneTensile.aviUsername: 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
0
20
40
60
80
100
120
140
160
180
0 0.01 0.02 0.03 0.04
Strain
Str
ess
(MP
a) Wet Bone
Critical Points on a generalized stress-strain curve
Determining the Yield Stress (Y) using 2% offset
MTS Test Results Mechanical Properties of Cortical Bone
Yield Point CalculationBone Tensile.xls
-50
0
50
100
150
200
0 0.01 0.02 0.03 0.04
Strain
Str
ess
(M
Pa)
Ystress = 135 MPaYsrain = 0.0077
E (0.1-0.3%)=23.45 GPa
MTS Test Results Mechanical Properties of Cortical Bone
Is the assumptionof linearity valid?
0.2% offset – Isit justified?
Modulus vs Strain (Tensile Test)
0
5
10
15
20
25
30
0 0.005 0.01 0.015 0.02 0.025 0.03
Strain
Mo
du
lus
(G
Pa)
Bone Tensile.xls
Yield Point
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
(GPa)
G
(GPa)
Ystrain
(%)
Ystress
(MPa)
U.Strain
(%)
U.Stress
(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)
Torsion 5.6
(0.8)
1.39
(0.24)
68
(7)
2.0
(0.15)
84
(11)
HypothesesBiomechanical 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*.
Link to Dry Bone Tensile Test FileUsername: biomed
Password: guest