HARMONIC DECOMPOSITION OF THE ANISOTROPIC ELASTICITY TENSOR

Backus (Rev. Geophys. Space Res. 8 (1970) 633) presents a theory on de composition of the elasticity tensor and its application in several pr oblems in anisotropy. The theory is supposed to be relatively difficul t. In this article, an illustration of the theory by examples is prese nted. Special attention is paid to the problem of deciding which kind of symmetry a material has when the elastic constants are measured rel ative to an arbitrary coordinate system. A second-order symmetric tens or associated to the elasticity tensor can be used to verify if the co ordinate axes are the symmetry axes of the medium, and determine a sym metry coordinate system. Also a comparison of Backus's theory with Cow ins's decomposition (Q. Jl Mech. appl. Math. 42 (1989) 249) is present ed. Uniqueness of the decompositions is specially discussed. Backus's decomposition is expressed here by means of the Voigt tensor, the dila tational modulus tensor and the traces of those two. Some misprints in Backus's expressions are indicated.