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	On symmetries and anisotropies of classical and micropolar linear elasticities: A new method based upon a complex vector basis and some systematic results
	Xiao, H
	1997
关键词	linear elasticities classical micropolar elasticity tensors symmetry anisotropy complex vector basis complex tensor TENSOR INVARIANTS REPRESENTATIONS DECOMPOSITION
英文摘要	A complete and unified study of symmetries and anisotropies of classical and micropolar elasticity tensors is presented by virtue of a novel method based on a well-chosen complex vector basis and algebra of complex tensors. It is proved that every elasticity tensor has nothing but 1-fold, 2-fold, 3-fold, 4-fold and oo-fold symmetry axes. From this fact it follows that the crystallographic symmetries plus the isotropic symmetry are complete in describing the symmetries of any kind of classical elasticity tensor and micropolar elasticity tensors. Further, it is proved that for each given integer m > 2 every classical Green elasticity tensor with an m-fold symmetry axis must have at least m elastic symmetry planes intersecting each other at this symmetry axis. From this fact and the aforementioned fact it follows that for all possible material symmetry groups, there exist only eight distinct symmetry classes for classical Green elasticity tensors, which correspond to the isotropy group and the seven crystal classes S-2, C-2h, D-2h, D-3d, D-6h and O-h, while it is shown that there exist twelve distinct symmetry classes for any other kind of elasticity tensors, including the classical Cauchy elasticity tensor and the micropolar elasticity tensors, which correspond to the eight subgroup classes just mentioned and the four crystal classes S-6, C-4h, C-6h and T-h. From these results, it turns out that all possible elasticity symmetry groups are nothing but the full orthogonal group, the transverse isotropy groups C-infinity h and D-infinity h, and the nine centrosymmetric crystallographic point groups except C-6h and D-6h.; Engineering, Multidisciplinary; Materials Science, Multidisciplinary; Mechanics; SCI(E); 0; ARTICLE; 2; 129-162; 49
语种	英语
出处	SCI
出版者	弹性学杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/219555]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xiao, H. On symmetries and anisotropies of classical and micropolar linear elasticities: A new method based upon a complex vector basis and some systematic results. 1997-01-01.

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