indentation of circular membrane

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  • jef
    Junior Member
    • Feb 2008
    • 2

    indentation of circular membrane

    Hi Steve,

    As a test model for further research, we’re trying to model the following experiment: an indentation in the center of a circular latex membrane, constrained at the edge. The radius of the membrane is 30 mm, height is 0.15 mm. Indentation is realized by a needle, from which the tip can be assumed to have a radius of 0.5 mm. The latex specimen is assumed to be linear elastic, having following properties: Young’s modulus 1.5e6 Pa and Poisson ratio 0.3 (estimated from literature). When the indentation is 5 mm, the measured reaction force on the needle is approximately 180 mN.

    As a first approach, the indentation was modeled by attaching a cubical rigid body (basis 0.5 mm) onto the center of the membrane. Next, the displacement of 5 mm on this rigid body is imposed, and the resulting reaction force on the rigid body is the output parameter of interest. The problem converged well (using more nodes resulted in converging to a constant reaction force), but the final value differs almost a factor 100 with the experimental value. Moreover, the resulting indentation-force curve is linear, while the experiment shows, as expected, a clearly nonlinear behavior.

    Further investigation didn’t result in a more realistic solution: placing the rigid body in the membrane instead of onto it using the tubal geometry (file1.feb), using shell elements by use of FEBio version 1.1 (file2.feb) or applying a pressure and taking a look at the resulting displacement all resulted in a significantly wrong output.

    As an additional test model, we tried to model the bending of a rectangular plate using shell elements. A quick look at the resulting deformation shows that there seems to be something wrong (as posted on this forum earlier).

    For comparison, we modeled the above mentioned problem in the Abaqus FEM-software packet, giving us results far more in agreement with the experimental data.

    You have any suggestions, remarks, … to obtain a more realistic solution?

    Thanks in advance!

    Cheers,
    Joris and Jef
  • maas
    Lead Code Developer
    • Nov 2007
    • 3400

    #2
    Hi guys,

    So, after looking at the code I don't see anything wrong with it, so I'm not sure why you are getting such different values than you were expecting. I guess my biggest critique to your approach is that you are comparing experimental results with a linear elastic model that is being applied outside the small strain regime. There is considerable bending that one may question the validity of this approach. My suspicion that this is part of the problem is made stronger by the observation that if you simply switch to a Neo-Hookean model for file1, the reaction force grows to about 50mN, which obviously is much closer to what you were expecting. As far as the shells are concerned I noticed that you did not prescribe a constraint on the rotational degrees of freedom at the boundary nodes (for file2). This will result in a hinged boundary condition, which is different than the clamped boundary condition implicitly enforced by your hex model and might explain why your shell model does not agree with your hex results.
    I'm sorry I can't be of more help. I will continue to run some test cases to make sure the rigid body reaction forces are calculated and reported accurately and if I do find anything that looks like a bug, I'll reply to this post. In the mean time I would suggest that you either decrease your deformation so that the small strian assumption is valid or start looking into some of the nonlinear materials that FEBio offers. You might also want to look into some problems for which the analytical solution is known and compare with that first, before trying to validate your models with experimental results.

    Cheers,

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

    Comment

    • jsoons
      Junior Member
      • Jan 2008
      • 10

      #3
      Originally posted by maas View Post
      Hi guys,
      As far as the shells are concerned I noticed that you did not prescribe a constraint on the rotational degrees of freedom at the boundary nodes (for file2). This will result in a hinged boundary condition, which is different than the clamped boundary condition implicitly enforced by your hex model and might explain why your shell model does not agree with your hex results.
      Hi Steve,

      Is it right that this didn't work for the moment with shell elements (because this was the reason that I posted the bug with the shell bending)?

      greets Joris

      Comment

      • maas
        Lead Code Developer
        • Nov 2007
        • 3400

        #4
        Hey Joris,

        For what you're doing you do have the option to provide clamped or hinged boundary conditions for shells. The problem you refer to only exists when coupling shells to rigid bodies. For that scenario you can only do hinged boundary condition for the moment.

        Cheers,

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

        Comment

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