Classification of symmetry by means of Maxwell multipoles
Open Access
- 1 February 1998
- journal article
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics
- Vol. 51 (1) , 73-104
- https://doi.org/10.1093/qjmam/51.1.73
Abstract
It is well known that elastic tensors are classified according to higher symmetry as monoclinic, orthorhombic etc. A classification into these classes by means of bouquets of space directions, called Maxwell's multipole, is given, and explicit expressions for the magnitudes of the directions are developed. The analysis is based on harmonic decomposition of the hierarchically symmetric tensor presented in Backus (Rev. Geophys. Space Phys. 8 (1970) 633-671), and further developed in Baerheim (Q. Jl Mech. appl. Math. 46 (1993) 391-418). Hierarchically symmetric tensors are defined as fourth rank tensors in three dimensions, satisfying the symmetry conditions Eijkl = Ejikl = Eijlk = Eklij. Software is developed to calculate the bouquets of space directions, and MATHEMATICA is used for displaying the results. As an example, multipoles are calculated for a specific tensor of monocline symmetry.Keywords
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