Proofs of only eight symmetry classes of a Hookean solid

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.

Bos, L., Slawinski, M.A., Stanoev, T., Vianello, M. (2020)   On orthogonal transformations of the Christoffel equations. International Journal on Geomathematics 11(6)


Bos, L., Slawinski, M.A., Stanoev, T. (2019)   On Christoffel roots for nondetached slowness surfaces. Geophysical Prospecting 67(9), 2280–2286


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


The Geomechanics Project