HARMONIC DECOMPOSITION OF THE ANISOTROPIC ELASTICITY TENSOR

Backus (Rev. Geophys. Space Res. 8 (1970) 633) presents a theory on decomposition of the elasticity tensor and its application in several problems in anisotropy. The theory is supposed to be relatively difficult. In this article, an illustration of the theory by examples is presented. Special attention is paid to the problem of deciding which kind of symmetry a material has when the elastic constants are measured relative to an arbitrary coordinate system. A second-order symmetric tensor associated to the elasticity tensor can be used to verify if the coordinate axes are the symmetry axes of the medium, and determine a symmetry coordinate system. Also a comparison of Backus's theory with Cowins's decomposition (Q. Jl Mech. appl. Math. 42 (1989) 249) is presented. Uniqueness of the decompositions is specially discussed. Backus's decomposition is expressed here by means of the Voigt tensor, the dilatational modulus tensor and the traces of those two. Some misprints in Backus's expressions are indicated.