relationship between bulk modulus and elastic constantby only1892 Tags: bulk, constant, elastic, modulus, relationship 

#1
May3107, 04:59 PM

P: 6

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
Jul2507, 07:33 AM

P: 136

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. Regards Modey3 



#3
Nov907, 03:38 AM

P: 70

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,pp349354. 


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