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	Some general properties of Eshelby's tensor fields in transport phenomena and anti-plane. elasticity
	Le Quang, H. ; He, Q. -C. ; Zheng, Q. -S.
	2010-05-07 ; 2010-05-07
关键词	transport phenomena thermal conduction Eshelby problem Eshelby tensor anti-plane elasticity inclusions anisotropy NON-ELLIPSOIDAL INCLUSIONS HEAT-CONDUCTION MEDIA SHAPE TRANSFORMATION SYMMETRY INFINITE Mechanics
中文摘要	Consider an infinite thermally conductive medium characterized by Fourier's law, in which a subdomain, called an inclusion, is subjected to a prescribed uniform heat flux-free temperature gradient. The second-order tensor field relating the gradient of the resulting temperature field over the medium to the uniform heat flux-free temperature gradient is referred to as Eshelby's tensor field for conduction. The present work aims at deriving the general properties of Eshelby's tensor field for conduction. It is found that: (i) the trace of Eshelby's tensor field is equal to the characteristic function of the inclusion, independently of the latter's shape; (ii) the isotropic part of Eshelby's tensor field over the inclusion of arbitrary shape is identical to Eshelby's tensor field over a 2D circular or 3D spherical inclusion; (iii) when the medium is made of an isotropic material and when the inclusion has some specific rotational symmetries, the value of the Eshelby's tensor field evaluated at the inclusion gravity center and the symmetric average of Eshelby's tensor fields are both equal to Eshelby's tensor field for a 2D circular or 3D spherical inclusion. These results are then extended, with the help of a linear transformation, to the general case where the medium consists of an anisotropic conductive material. The method elaborated and results obtained by the present work are directly transposable to the physically analogous transport phenomena of electric conduction, dielectrics, magnetism, diffusion and flow in porous media and to the mathematically identical phenomenon of anti-plane elasticity. (C) 2007 Elsevier Ltd. All rights reserved.
语种	英语 ; 英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD ; OXFORD ; THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/16221]
专题	清华大学
推荐引用方式 GB/T 7714	Le Quang, H.,He, Q. -C.,Zheng, Q. -S.. Some general properties of Eshelby's tensor fields in transport phenomena and anti-plane. elasticity[J],2010, 2010.
APA	Le Quang, H.,He, Q. -C.,&Zheng, Q. -S..(2010).Some general properties of Eshelby's tensor fields in transport phenomena and anti-plane. elasticity..
MLA	Le Quang, H.,et al."Some general properties of Eshelby's tensor fields in transport phenomena and anti-plane. elasticity".(2010).

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