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Thread: Cell Growth: Growth and Buckling

  1. #1
    Join Date
    Dec 2007
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    Default Cell Growth: Growth and Buckling

    This example is the last in a series illustrating the "cell growth" material in FEBio. To better understand the material presented here, please refer to the examples on Single Cell Growth, Internal Constraints to Growth, and External Constraints to Growth.

    This last example demonstrates the interesting combination of growth and buckling. This example is inspired by a presentation I saw by Oliver Jensen, of the University of Nottingham, titled "Multiscale models for tissue growth: from epithelium to epidermis" and given at the Workshop in Microscale Modeling in Biomechanics and Mechanobiology, held at Ericeira, Portugal, May 30-June 1, 2011.


    Consider a beam fixed at both ends, consisting of a "solid mixture" with a "neo-Hookean" solid matrix (Young's modulus = 1 kPa) and "cell growth" material, where cells grow fivefold.
    (click on image to see movie)
    BeamNoBuckling.feb
    If there are no other constraints on the beam, the growth will simply consist of an apparent swelling, albeit constrained at the fixed ends.

    (click on image to see movie)
    BeamBuckling.feb
    Now consider a disturbance in the form of a small force, temporarily nudging the beam upward at its center, while growth is proceeding. As a result of this small disturbance, the beam buckles during growth and takes on a very different shape, as shown in the attached movie. This form of growth is reminiscent of the process of invagination during morphogenesis.

    (click on image to see movie)
    BeamBucklingStiffer.feb
    Buckling is an instability which may exhibit multiple modes. In this last example, the Young's modulus of the beam is increased to 10 kPa. All else remaining the same, the resulting buckling behavior exhibits multiple folds, as shown in the attached movie.

    This last series of example further demonstrates the rich set of outcomes that may be achieved with the "cell growth" model implemented in FEBio. Buckling analyses under finite deformation are not trivial problems in a finite element framework. The files attached with these examples will exhibit slow convergence, but they should run to completion.

    If you try the cell growth model and get cool results, feel free to share them on this forum.

    Gerard

  2. #2

    Default

    Hi dear Gerard

    I could't see the images which you mentioned to watch the movies. are they here in your posts?

  3. #3

    Default

    Dear Gerard
    I have another question. your model belongs to an older version of FEBio. your .feb file has a section for loads as following:
    <force>
    <node id="1101" bc="y" lc="2">1</node>
    <node id="1102" bc="y" lc="2">1</node>
    </force>
    this section has been changed in next vesrsions.
    I tried this one accordig to the manual:
    <nodal_load bc="y" lc="2">
    <node id="1101">1</node>
    <node id="1102">1</node>
    </force>
    but it doesn't work.
    as I tried to find the replace code in febio2 for this section, I didn't succeed. so the code doesn't work. could you please help me that how should I change this section in the new version in such a way that it runs correctly?
    Best,
    Faezeh

  4. #4
    Join Date
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    Salt Lake City, UTAH
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    Default

    Hi Faezeh,

    The easiest way to convert older FEBio input files to the new format is via PreView. You should be able to read in the old files and then export it to the new format. Give that a try and let us know if that worked. At our end, we'll try to find some time to update this post and the files.

    Cheers,

    Steve
    Department of Bioengineering, University of Utah
    Scientific Computing and Imaging institute, University of Utah

  5. #5

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    Hi Steve
    what do you mean exactly? do you mean that I should rebuild the model with preview? I would give it a try but I don't have the dimensions!!

  6. #6
    Join Date
    Nov 2007
    Location
    Salt Lake City, UTAH
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    Default

    Hi Faezeh,

    I am not proposing to rebuild the model from scratch. Instead, you could download the files here (using the older formats), import them into PreView (from file menu File\Import) and then export the model back (from file menu File\Export) in the new format. You should not need to make any changes to the model. I hope that explains it better.

    Cheers,

    Steve
    Department of Bioengineering, University of Utah
    Scientific Computing and Imaging institute, University of Utah

  7. #7

    Default

    oh, thanks a lot for your explanations. now it works!
    best
    Faezeh

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