The arithmetic mean theorem of Eshelby tensor for exterior points   outside the rotational symmetrical inclusion

doi:10.1115/1.2165238

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	The arithmetic mean theorem of Eshelby tensor for exterior points outside the rotational symmetrical inclusion
	Wang, Min-Zhong ; Xu, Bai-Xiang
刊名	journal of applied mechanics transactions of the asme
	2006
关键词	QUANTUM-WIRE STRUCTURES STRAIN DISTRIBUTIONS POLYGONAL INCLUSION ARBITRARY SHAPE FIELD PROPERTY DOTS
DOI	10.1115/1.2165238
英文摘要	In 1957, Eshelby proved that the strain field within a homogeneous ellipsoidal inclusion embedded in an infinite isotropic media is uniform, when the eigenstrain prescribed in the inclusion is uniform. This property is usually referred to as the Eshelby property. Although the Eshelby property does not hold for the non-ellipsoidal inclusions, in recent studies we have successfully proved that the arithmetic mean of Eshelby tensors at N rotational symmetrical points inside an N-fold rotational symmetrical inclusion is constant and equals the Eshelby tensor for a circular inclusion, when N >= 3 and N not equal 4. The property is named the quasi-Eshelby property or the arithmetic mean theorem of Eshelby tensors for interior points. In this paper, we investigate the elastic field outside the inclusion. By the Green formula and the knowledge of complex variable functions, we prove that the arithmetic mean of Eshelby tensors at N rotational symmetrical points outside an N-fold rotational symmetrical inclusion is equal to zero, when N >= 3 and N not equal 4. The property is referred to as the arithmetic mean theorem of Eshelby tensors for exterior points. Due to the quality of the Green function for plane strain problems, the fourfold rotational symmetrical inclusions are excluded from possessing the arithmetic mean theorem. At the same time, by the method proposed in this paper, we verify the quasi-Eshelby property which has been obtained in our previous work. As corollaries, two more special properties of Eshelby tensor for N-fold rotational symmetrical inclusions are presented which may be beneficial to the evaluation of effective material properties of composites. Finally, the circular inclusion is used to test the validity of the arithmetic mean theorem for exterior points by using the known solutions.; Mechanics; SCI(E); EI; 0; ARTICLE; 4; 672-678; 73
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/316169]
专题	工学院
推荐引用方式 GB/T 7714	Wang, Min-Zhong,Xu, Bai-Xiang. The arithmetic mean theorem of Eshelby tensor for exterior points outside the rotational symmetrical inclusion[J]. journal of applied mechanics transactions of the asme,2006.
APA	Wang, Min-Zhong,&Xu, Bai-Xiang.(2006).The arithmetic mean theorem of Eshelby tensor for exterior points outside the rotational symmetrical inclusion.journal of applied mechanics transactions of the asme.
MLA	Wang, Min-Zhong,et al."The arithmetic mean theorem of Eshelby tensor for exterior points outside the rotational symmetrical inclusion".journal of applied mechanics transactions of the asme (2006).