CLASSIFICATION OF SYMMETRY BY MEANS OF MAXWELL MULTIPOLES

It is well known that elastic tensors are classified according to high er symmetry as monoclinic, orthorhombic etc. A classification into the se classes by means of bouquets of space directions, called Maxwell's multipoles, is given, and explicit expressions for the magnitudes of t he directions are developed. The analysis is based on harmonic decompo sition of the hierarchically symmetric tensor presented in Backus (Rev . Geophys. Space Phys. 8 (1970) 633-671), and further developed in Bae rheim (Q. Jl Mech. appl. Math. 46 (1993) 391-418). Hierarchically symm etric tensors are defined as fourth rank tensors in three dimensions, satisfying the symmetry conditions E-ijkl = E-jikl = E-ijlk E-klij. So ftware is developed to calculate the bouquets of space directions, and MATHEMATICA is used for displaying the results. As an example, multip oles are calculated for a specific tensor of monoclinic symmetry.