Orientation distribution functions for microstructures of heterogeneous materials (II) - Crystal distribution functions and irreducible tensors restricted by various material symmetries

Authors
Citation
Qs. Zheng et Yb. Fu, Orientation distribution functions for microstructures of heterogeneous materials (II) - Crystal distribution functions and irreducible tensors restricted by various material symmetries, APP MATH ME, 22(8), 2001, pp. 885-903
Citations number
18
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mechanical Engineering
Journal title
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
ISSN journal
0253-4827 → ACNP
Volume
22
Issue
8
Year of publication
2001
Pages
885 - 903
Database
ISI
SICI code
0253-4827(200108)22:8<885:ODFFMO>2.0.ZU;2-9
Abstract
The explicit representations for tensorial Fourier expansion of 3-D crystal orientation distribution functions (CODFs) are established. In comparison with that the coefficients in the mth term of the Fourier expansion of a 3- D ODF make up just a single irreducible mth-order tensor, the coefficients in the mth term of the Fourier expansion of a 3-D CODF constitute generally so many as 2m, + 1 irreducible mth-order tensors. Therefore, the restricte d forms of tensorial Fourier expansions of 3-D CODFs imposed by various mic ro- and macro-scopic symmetries are further established, and it is shown th at in most cases of symmetry the restricted forms of tensorial Fourier expa nsions of 3- D CODFs contain remarkably reduced numbers of mth-order irredu cible tensors than the number 2m + 1. These results are based on the restri cted forms of irreducible tensors imposed by various point-group symmetries , which are also thoroughly investigated in the present part in both 2- and 3-D spaces.