We presented proofs that show that there are only eight symmetry classes of a Hookean solid, and that their hierarchy is only partially ordered.  

 

Our proofs are based on group theory.

 

Without this work, many seismologists implicitly assumed that there would be a possibility of extending the number of symmetry classes as could be necessary to accommodate modelling needs.  

 

Also, many seismologists assumed a sequential hierarchy proceeding from the general anisotropy to isotropy.  

 

The recognition of these intrinsic properties of a Hookean solid allows for a reliable interpretation of seismic models, which — for the most part — are based on such a solid.

Bóna, A., Diner, Ç., Kochetov, M., Slawinski, M.A.  (2010)   On symmetries of elasticity tensors and Christoffel matrices .   arXiv:1011.4975

 

Bóna, A., Bucataru, I., Slawinski, M.A.  (2008)   Space of SO(3)-orbits of elasticity tensors .   Archives of Mechanics 60(2), 121–136

 

Bóna, A., Bucataru, I., Slawinski, M.A.  (2004)   Characterization of elasticity-tensor symmetries using SU(2).   Journal of Elasticity 75(3), 267–289

 

Bóna, A., Bucataru, I., Slawinski, M.A.   (2004)   Material symmetries of elasticity tensors .  The Quarterly Journal of Mechanics and Applied Mathematics 57(4), 583–598

 

Bos, L.P., Gibson, P.C., Kochetov, M., Slawinski, M.A.   (2004)   Classes of anisotropic media: A tutorial.   Studia Geophysica and Geodætica 48, 265–287

 

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