非均匀材料细观结构的定向分布函数(Ⅱ)——晶体分布函数和各种材料对称性约束下的不可约张量

郑泉水; 傅依斌

非均匀材料细观结构的定向分布函数(Ⅱ)——晶体分布函数和各种材料对称性约束下的不可约张量

郑泉水¹,
傅依斌²

1.
清华大学工程力学系, 北京 100084;
2.
基勒德大学数学系, 斯塔福郡 ST586, 英国

基金项目: 国家自然科学基金资助项目(19525207;19891180);霍英东教育基金资助项目

详细信息

作者简介:
郑泉水(1961- ),男,江西人,教授,博士,教育部长江特聘教授.

中图分类号: O331
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- 被引次数: 0
出版历程
- 收稿日期: 2000-10-09
- 修回日期: 2001-03-20
- 刊出日期: 2001-08-15

Orientation Distribution Functions for Microstructures of Heterogeneous Materials(Ⅱ)-Crystal Distribution Functions and Irreducible Tensors Restricted by Various Material Symmetries

ZHENG Quan-shui¹,
FU Yi-bin²

1.
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P R China;
2.
Department of Mathematics, University of Keele, Staffordshire, ST5 586, UK

摘要

摘要: 目的是建立三维晶体定向分布函数(CODF)的张量傅立叶展开的显式表示.与三维ODF的傅立叶展开的第m项系数仅对应单个m阶对称无迹张量不同,三维CODF的傅立叶展开的第m项系数一般由2m+1个m阶对称无迹张量组成.随后还建立了在各种宏观和微观对称性下三维CODF的张量傅立叶展开的约束形式,表明大多数对称性下的约束形式中的m阶不可约张量数目明显少于2m+1.这些结果是通过对各种点群对称性约束下二维和三维不可约张量的约束形式的研究得到的.
- 晶体定向分布函数 /
- 不可约张量 /
- 傅立叶展开 /
- 细观结构 /
- 材料对称性
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 m th-term of the Fourier expansion of a 3-D ODF make up just a single irreducible m th order tensor,the coefficients in the m th term of the Fourier expansion of a 3-D CODF constitute generally so many as 2m+1 irreducible m th order tensors.Therefore,the restricted forms of tensorial Fourier expansions of 3-D CODFs imposed by various microand 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 m th order irreducible tensors than the number 2m+1.These results are based on the restricted forms of irreducible tensors imposed by various pointgroup symmetries,which are also thoroughly investigated in the present part in both 2and 3-D spaces.
- crystal orientation distribution function /
- irreducible tensor /
- Fourier expansion /
- microstructure /
- material symmetry

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参考文献(22)

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