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using qlv with bi-linear data

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  • using qlv with bi-linear data

    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,

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    William R. Ledoux
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