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 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.
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Zheng, Qs., Fu, Yb. Orientation Distribution Functions for Microstructures of Heterogeneous Materials (II)—Crystal Distribution Functions and Irreducible Tensors Restricted by Various Material Symmetries. Applied Mathematics and Mechanics 22, 885–903 (2001). https://doi.org/10.1023/A:1016338225737
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DOI: https://doi.org/10.1023/A:1016338225737