Characterization of elasticity-tensor symmetries using SU(2)

Journal of Elasticity

Volumn 75, Issue 3, 2004, Pages 267-289

  Bóna, Andrej ^a   Bucataru, Ioan ^b   Slawinski, Michael A ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

^b ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

Elasticity tensor; Group theory; SU(2); Symmetry classes

Indexed keywords

COMPUTATIONAL COMPLEXITY; MAXWELL EQUATIONS; POLYNOMIALS; SET THEORY; TENSORS; VECTORS;

ELASTICITY TENSOR; GROUP THEORY; SU(2); SYMMETRY CLASSES;

ELASTICITY;

EID: 13944271052     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-004-7192-0     Document Type: Article

References (16)

1. G. Backus, A geometrical picture of anisotropic elastic tensors. Rev. Geophys. Space Phys. 8(3) (1970) 633-671.
2. R. Baerheim, Coordinate free representation of the hierarchically symmetric tensor of rank 4 in determination of symmetry. PhD Thesis. Geologica Ultraiectina 159 (1998).
3. A. Bóna, I. Bucataru, M.A. Slawinski, Material symmetries of elasticity tensors. Quart. J. Mech. Appl. Math. (in press).
4. L.P. Bos, P.C. Gibson, M. Kotchetov and M.A. Slawinski, Classes of anisotropic media: A tutorial. Studio Geophysica Geodaetica 48 (2004) 265-287.
5. P. Chadwick, M. Vianello and S.C. Cowin, A new proof that the number of linear elastic symmetries is eight. J. Mech. Phys. Solids 49 (2001) 2471-2492.
6. S.C. Cowin and M.M. Mehrabadi, On the identification of material symmetry for anisotropic elastic materials. Quart. J. Mech. Appl. Math. 40 (1987) 451-476.
7. S.C. Cowin and M.M. Mehrabadi, The structure of the linear anisotropic elastic symmetries. Mech. Phys. Solids 40(7) (1992) 1459-1471.
8. M. Crampin and F.A.E. Pirani, Applicable Differentiable Geometry. Cambridge Univ. Press, Cambridge (1994).
9. S. Forte and M. Vianello, Symmetry classes for elasticity tensors. J. Elasticity 43(2) (1996) 81-108.
10. S. Forte and M. Vianello, Symmetry classes and harmonic decomposition for photoelasticity tensors. Internat. J. Engrg. Sci. 35(14) (1997) 1317-1326.
11. B. Herman, Some theorems of the theory of anisotropic media. Comptes Rendus (Doklady) Acad. Sci. URSS 48(2) (1945) 89-92.
12. Y.Z Huo and G. del Piero, On the completeness of the crystallographic symmetries in the description of the symmetries of the elastic tensor. J. Elasticity 25 (1991) 203-246.
13. M.A. Slawinski, Seismic Rays and Waves in Elastic Media. Pergamon, New York (2003).
14. T.C.T. Ting, Generalized Cowin-Mehrabadi theorems and a direct proof that the number of linear elastic symmetries is eight. Internat. J. Solids Struct. 40 (2003) 7129-7142.
15. H. Xiao, On symmetries and anisotropies of classical and micropolar linear elasticities: A new method based upon a complex vector basis and some systematic results. J. Elasticity 49 (1998) 129-162.
16. W.N. Zou and Q.S. Zheng, Maxwell's multipole representation of traceless symmetric tensors and its application to function of high-order tensors. Proc. Roy. Soc. London 459 (2003) 527-538.