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model curve-fit of mechanical properties from indentation testing

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  • model curve-fit of mechanical properties from indentation testing

    I am a student doing my masters thesis at the Beth Israel Deaconess
    Medical Center in Boston, USA. I have to do some indentation testing on
    the outer part of intervertebral discs, the Annulus Fibrosus. It is a
    fibrous soft tissue. The samples are composed of single lamellae, which
    are between 0.4 and 1 mm thick. The aim is to get the mechanical
    properties (Youn's modulus, Poisson's ratio and permeability) from a
    stress-relaxation test. Usually, one uses a non-linear elastic biphasic model to
    describe the behavior of the Annulus Fibrosus (Ateshian et al., 1997, J
    Biomechanics; Perie et al., 2006, Annals of Biomedical Engineering).
    The permeability k of the tissue is given by: dsigma/depsilon * d2u/dz2 =
    epsilon/k * du/dt, where sigma is the stress, epsilon the stretch, u
    the displacement, z the vertical coordinate and t the time. My problem
    and question is 1) how to compute the d2u/dz2 term when one does a
    stress-relaxation test. I found no explanation in the articles I have read
    so far. Because the displacement equals the z coordinate I don't see how
    this term is not equal to zero. Would anyone have an idea on how to
    solve this? and 2) is the aggregate modulus, HA0, normally determined
    under confined compression? or can it also be determined under non-confined

    Thanks in advance.
    Alexandre Sabben
    Research Assistant
    Beth Israel Deaconess Medical Center
    Boston, MA, USA

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