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

Autor: Quan-shui, Zheng, Yi-bin, Fu
Předmět:
Zdroj: Applied Mathematics & Mechanics; Aug2001, Vol. 22 Issue 8, p885-903, 19p
Abstrakt: 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 restricted forms of tensorial Fourier expansions of 3-D CODFs imposed by various micro- and macro-scopic symmetries are further established, and it is shown that in most cases of symmetry the restricted forms of tensorial Fourier expansions of 3-D CODFs contain remarkably reduced numbers of mth-order irreducible tensors than the number 2m+1. These results are based on the restricted 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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