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• W2073458200 abstract "The strain field ɛ(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ɛ0 in a domain ω depends linearly upon ɛ0:ɛij(x)=Sijklω(x)ɛkl0. It has been a long-standing conjecture that the Eshelby's tensor field Sω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. Because of the minor index symmetry Sijklω=Sjiklω=Sijlkω, Sω might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of Sω, we show that the isotropic part S of Sω vanishes outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part Aω=Sω-S of Sω is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ω's geometry. Remarkably, the above irreducible structure of Sω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of Sω at the center of a 2D Cn(n⩾3,n≠4)-symmetric or 3D icosahedral ω and the average value of Sω over such a ω are equal to S0." @default.
• W2073458200 created "2016-06-24" @default.
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• W2073458200 creator A5083186038 @default.
• W2073458200 creator A5085406295 @default.
• W2073458200 date "2006-02-01" @default.
• W2073458200 modified "2023-10-06" @default.
• W2073458200 title "Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity" @default.
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• W2073458200 doi "https://doi.org/10.1016/j.jmps.2005.08.012" @default.
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