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Thread: Strain at boundaries of biphasic-solute model

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  1. #1
    Join Date
    Feb 2015
    Posts
    6

    Default Strain at boundaries of biphasic-solute model

    Hi,

    I've created a biphasic-solute model of free swelling of the cartilage and have a few questions about the strain data. My cartilage model is a simple cube divided into 3 layers with 2 different values of Young's Modulus (1st layer Young's Modulus = 10Mpa, 2nd layer Young's Modulus = 20Mpa, 3rd layer Young's Modulus = 20Mpa; the boundaries between the layers are refined). All sides are constrained apart from the top layer where I apply my concentration and strain over 1hr (the model can only expand in the z-direction).
    The model is working fine, I can see the swelling and the increase in concentration. However, when I plot the strain data, the strain is discontinuous at the boundaries (I used Z Lagrange strain). On the other hand, the displacement plots look fine, and I don't know whether I'm just using the wrong strain data for this? I've attached the relevant figures

    Any insight into this would be much appreciated,

    Many thanks.
    Kinga
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  2. #2
    Join Date
    Nov 2007
    Location
    Park City, Utah
    Posts
    121

    Default

    Because you have different material properties in the two layers of adjacent elements at the interface, the stress and strain will be discontinuous at the interface. In the finite element method, only the nodal variables are typically guaranteed to be continuous across elements. In this case displacement, pressure are the relevant nodal variables. However their derivatives will not be continuous across element boundaries. Strain is obtained from the gradient of the displacement field, and stress is obtained from strain, so neither quantity will be continuous in general.

    Best regards,

    Jeff Weiss
    Jeff Weiss
    Professor, Department of Bioengineering, University of Utah
    Director, Musculoskeletal Research Laboratories
    jeff.weiss@utah.edu

  3. #3
    Join Date
    Feb 2015
    Posts
    6

    Default

    Thank you very much for the clarification. Now I understand.

    Regards,
    Kinga

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