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