== MS_polyaverage

 MS_POLYAVERAGE - Isotropic elasticity for polycrystal 

 // Part of MSAT - The Matlab Seismic Anisotropy Toolkit //

 Calculate the bulk and shear moduli of an isotropic polycrystal. 

 [ K_vrh, G_vrh, ... ] = MS_polyavarage( C )

 Usage: 
     [ K_vrh, G_vrh ] = MS_polyavarage( C )                    
         Return Voigt-Reuss-Hill avarage bulk (K) and shear (G) moduli of 
         an isotropic aggregate composed of randomly orentated ansiotropic
         crystals described by the elasticity matrix C.

     [ K_vrh, G_vrh, K_v, G_v, K_r, G_r ] = MS_polyavarage( C )
         Also return Voigt and Reuss bounds on the bulk and shear moduli.

 Notes:
     For the case of an isotropic solid formed from a random distribution
     of elements, the bulk and shear moduli can be found directly without
     the need to rotate the crystal. See Anderson, Theory of the Earth,
     pp. 122.


 See also: MS_VRH, MS_ANISOTROPY
