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Linear elastic -> Hyperelastic coefficient conversion

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  • Linear elastic -> Hyperelastic coefficient conversion

    Hello,

    I am currently working on modeling soft tissue. I got as only data the Young modulus E=2500 Pa and the poisson ration =0.499 (incompressible material).

    They ask me to work with the hyperelastic model so I need to understand if the is an equivalence between hyperelastic and linear elastic coefficient. I will be working with Mooney rivlin model so I need C_10 and C_01.
    Can someone help me?

    Regards
    David

  • #2
    If all you know are E and nu (and you cannot perform additional tests), then you should not use a Mooney-Rivin model but a Neo-Hookean model.

    The shear modulus for the NH model is E/3.

    -Jorgen
    Jorgen Bergstrom, Ph.D. PolymerFEM Administrator

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    • #3
      Originally posted by Jorgen View Post
      If all you know are E and nu (and you cannot perform additional tests), then you should not use a Mooney-Rivin model but a Neo-Hookean model.

      The shear modulus for the NH model is E/3.

      -Jorgen
      Thank you very much for this answer. Is there a paper/book where I can get this information in order to cite it?

      David

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      • #4
        You can site me

        It is actually easy to derive (perhaps you don't need to cite it):

        :arrow: The Poisson't ratio of most rubbers and soft tissues is typically close to 0.5 (that is incompressible).

        :arrow: The shear modulus is given by (see most intro to solid mechanics books):
        mu = E / (2 * (1 + nu))

        If you insert nu=0.5 you will get mu = E/3...

        -Jorgen
        Jorgen Bergstrom, Ph.D. PolymerFEM Administrator

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        • #5
          What is the incompressibility parameter used in Neo-Hooken model ? how to derive it?

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          • #6
            Hello Dr. Jorgen

            As i told you, I have hardness value for rubber and nu = 0.5(rubber is incompressible). You asked me use Neo-Hookean form. I needed two parameters C10 and D1

            So I converted hardness 's' into E as per ref formula E = 0.0981(56+7.62336s)/0.137505(254-2.54s)

            I will get Shear modulus 0 = E/2(1+nu). and from this i will calculate C10 = 0/2

            D1 = 0 for incompressible in abaqus/standard,

            So I will have both C10 and D1

            please tell me if this approach is right....

            Thank you in advance..
            Last edited by sandeep18784; 2011-10-08, 18:01.

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            • #7
              That sounds right.

              -Jorgen
              Jorgen Bergstrom, Ph.D. PolymerFEM Administrator

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              • #8
                Hello jorgen

                Can you tell How can we find out C_10 and D_1 experimentally?

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