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William R. Ledoux Ii
07-23-1996, 01:35 PM
Dear Biomech-lers,

Several months ago I posted the following question:

Is anyone aware of a protocol that allows for the development of
a constitutive relationship for soft tissue under shear and compression
simutaneously?

I received several responses (summarized below), but I did not
come across an answer that provided the specific information that I was
interested in obtaining. I will rephrase my question.


Is anyone aware of any work (experimental or theoretical) in which
a material is SIMULTANEOUSLY loaded in shear and compression? For
example, has anyone actually worked out Fung's 1-dimensional
quasilinear theory for 2- or 3-dimensions? I am interested in the jig
design, the test protocol, and the use of the data to develop a
constitutive relationship for the material in both shear and
compression?


Many thanks to those who responded already.

Bil Ledoux
wrledoux@eniac.seas.upenn.edu

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I read your posting with considerable interest, not because I have
any answers for you, but because I am faced with many of the same
problems you have mentioned. Are you interested in heel pad properties
for specific patient groups? (e.g. diabetic patients?)

We have developed a device here for measuring both shear and pressure
on the plantar surface of the foot as a persons walks across a matrix
of sensors. At the moment these sensors measure 1 inch x 1 inch, but
we are presently designing a device with greater spatial resolution.

Have you considered developing a finite element model of the heel
region and then altering the material properties of the soft tissue
until your predicted deformations match those obtained experimentally?
This would provide indirect estimates of the material properties.

In the work we are doing here, we are trying to model the foot, apply
(measured) pressure and shear to the model, and then compare predicted
compression with ultrasound data that show dynamic soft tissue
compression during gait.

I look forward to seeing your other responses,
Brian
-------------------------------------
Name: Brian L. Davis, PhD
E-mail: davis@bme.ri.ccf.org

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Considereble undertaking for the heel pad.
We have looked after patients with heel pain and some normal patients as
controls, there is considereble difference in the amount of soft tissue
compression that we could measure rediologically and there was so many
bias that we stopped considering it for publication because we had some
problems in obtaining standardised X-rays. The difference changes with
the age of the patient and whether the patient has hell pain or not.
I would advise you to find cadavers with similar age group that you want
your imply your results to show.

Yal=FDm Ates MD
Orthopaedic Surgeon

yates@neuron.ato.org.tr

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Dear Bil,

The most elegant experimental protocol I have ever seen, and arguably the
best around is by Jay Humphrey at U. Maryland. His specialty is for
vascular and myocardial tissue, but the same principles are directly
applicable. I do not have his address, but I am sure you can find it on
the net.

J.F. Antaki, PhD
University of Pittsburgh


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To answer your question, it is certainly possible to construct a model
to deal with 3-d quasilinear data. You must use a tensor form. (Yes,
Badderman's course finally has a use for you...) You'll get a constitituve
equation that can combine any sort of elastic behaviour, (I use hyperelastic
usually) with the viscoelastic behaviour. Then you can use any kind
of experimental data you like, eg compressive + shear to find your best
fit for data. The best place to look to see examples of this is in
the rheology literature rather than bioengineering literature. They don't
explicitly use fung's exact form, but his form is equivalent to boltzmann's
viscoelasticity formulation. Polymers and bread doughs are good examples
of things to look for. I shall endeavour to find you a good reference on
this.
Try looking up on compendex on CDrom in the engineering library rather than
on medline.

For practical purposes of experiments, I use a combination of tensile
relaxation tests, oscillating shear tests, and a cool new test which is
an oscillating compressive test done with random noise oscillations,
which (through various mathematics) allows you you do a 10 minute test
from which you can pull out the entire relaxation spectrum of the material.
You can then choose your relaxation time constants and use the relaxation
modulus as a sum of exponentials with those time constants as relaxation
times. Essentially, you measure the G' and G'' as functions of frequency
and use
that data to to calculate the relaxation spectrum numerically. I think
Kristy said she has done some oscillating shear experiments on her brain
tissue, and made a constitutive model. Did you talk to her?

If you don't understand a word of this, reply and I'll try to be clearer.

Lynne
__________________________________________________ ________________________
Lynne E. Bilston, PhD
Department of Mechanical and Mechatronic Engineering Tel (02) 351-2344
Room 311, Building J07 Fax (02) 351-7060
University of Sydney, N.S.W., 2006 bilston@tiny.me.su.oz.au
AUSTRALIA
http://www.me.su.oz.au/staff/bilston.html
__________________________________________________ ________________________


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Hi,
And in the elementary solutions, you can "layer" additional levels of
complexity to add in the effects of viscoelasticity, such as using
Fung's Law or other semi-empirical curve fits.

good luck!
doug


Hi,
Any elementary contact mechanics textbook or elasticity book will routinely
discuss the effect of compression, shear and bending moments.

doug