Materials Characterization Project
Part A: Material Characterization of Cartilage
You are working in a research lab performing viscoelastic characterization of cartilage using indentation test to obtain its
material properties. An underpaid graduate student has done the majority of the analysis and converted the data into
the force relaxation form. However, due to a lack of money and the increasing health care costs, the graduate student
cannot afford a new laptop, and the 486 laptop with Windows 3.1 does not have enough processing power to run
Matlab or excel to perform the curve fitting
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optimization. The grad student is seeking your help
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with the data analysis by hand (Do NOT use a
computer or do the curve fitting). You are told to
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use a single time constant Maxwell Model with a
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force relaxation response of:
Determine the coefficients of the material model:
B∞, B1, and τ1 without the use of a computer curve
fit solver/optimizer.
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Force/Stress
F (t )  B  B1e t /1
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1.0
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Part B: Structural Experimental Response on
Cartilage
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The graduate student wants to perform tensile tests
on cartilage for a presentation at a conference. The
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abstract was already submitted last semester, prior
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to knowing that attempting these tensile test
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time(s)
experiments on cartilage were a bad idea. Cartilage
samples were painstakingly prepared such that for the given geometry, its force responses exactly matched the
relaxation function for a given level of strain/displacement. The experiments were an utter failure, as all the cartilage
samples fell out of the grips, and no meaningful data was collected. However, the grad student still needs some data to
present at the conference (February 19th, 2025 aka Assignment Due Date). Taking what you have learned from lectures,
you suggest using the material properties (stress/force relaxation function) of the cartilage to simulate the force output
for a given strain input.
The graduate student provides you with a force relaxation function for the cartilage as:
F (t )  2  2.5e  t /1.25
The graduate student needs simulated data for the set of loading experiments shown on the back.
Determine the theoretical force-time response for each of these loading experiments on the cartilage. Make to plot
each response for at least 8 seconds.
*Hint #1* You may draw these by hand, or generate them computationally. One method may be easier than the other
for a particular loading scenario.
*Hint #2* It is possible for the forces to go negative (so make sure your plot axes show this). This is OK, as it is just a
compressive force instead of a tensile force.
1. Single Step loading and hold
3. Two-step loading
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strain/displacement
strain/displacement
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4. Ramp Loading with a slope of 1
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strain/displacement
strain/displacement
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0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
time(s)
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time(s)
2. Single Step loading and return to initial position
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time(s)
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time(s)
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