Relationship between bulk modulus and elastic constant

  1. I am getting the bulk modulus from fitting the equation of states and calculating the elastic constant. It seems that there is some relationship between bulk modulus B and elastic constant Cij, B=Cij/9,where i,j run from 1 to 3.
    But my result is far away from this, say B=50 from fitting EOS and B=300 from elastic constant. Is this resonable or B=Cij/9 cann't be applied to some material(structure)?

    Thanks a lot!
  2. jcsd
  3. The relationship between the bulk modulus and the elastic constants is:

    B = 1/3 (C11 + 2*C12) for polycrystalline, isotropic cubic crystals

    If the material has lower symmetry like a orthorhombic material it would have more independent elastic constants. Remember the concept of the bulk modulus was developed for polycrystalline material only. Not that single crystals don't resist volumetric distortion - of course they do. This resistance is going to be system specific and to give further details I need more info.


  4. To add, if the system is not cubic, there are two possibilities for the polycrystalline Bulk Modulus from the elastic constants.

    Voight Average:

    9B = ( c11 + c22 + c33 ) + 2*(c12 + c13 + c23)

    Reuss Average

    1/B = ( s11 + s22 + s33 ) + 2*(s12 + s13 + s23);

    Details in the paper

    "The Elastic Behaviour of a Crystalline Aggregate", by R.Hill.

    Proceedings of the Physical Society of London, Section A. Vol 65, No 5. May 1952,pp349-354.
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