using qlv with bi-linear data

[William Ledoux]

Biomch-lers,
I am interested in employing Fung's quasi-linear viscoelastic theory
to curve
fit stress relaxation data. I am preforming a compression test whereby I ramp
to a certain displacement and hold while I am measuring the force. My
question concerns the approach employed for the reduced relaxation response (I
will call this G from here on). Fung's text books (1972 and 1993) and many
articles in the literature (e.g., Woo, J. Biomech. Eng., 1981, Kwan, J.
Biomech, 1993, and Myers, J. Biomech, 1994) all demonstrate a linear results
for G. By that, I mean that on a semi log plot of the G, the data are
approximately linear between 2 points refered to as tau1 and tau2. (see plot
below on the left) These constants are two time constants. Fung details how
to solve for tau1, tau2 and the third constant (c) by using three equations (G
at 1 sec, G at infinitely (the end of the experiment) and the slope of G).
My specific question is what can be done if the data is not linear? (see
plot below on the right) When I plot G with the log of time I get a
distinctly bi-linear curve. Does anyone have any experience curve fitting
with bi-linear stress relaxation data such as this? I am considering the not
using Fung's form of G and instead using a multiple exponential fit.

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tau1 tau2

typical, linear curve
bilinear response

These plots are crude, but they demonstrate my point.



thanks for the help,

Bil
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William R. Ledoux
PCPM
Gait Study Center
8th and Race Streets
Philadelphia, PA 19107
wrledoux@eniac.seas.upenn.edu
215-629-0300 0 for the operator, ext. 6064

"No matter how small the effort, progress is measured by doing something every day."

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