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首页> 外文会议>Japan International SAMPE Symposium and Exhibition >ESHELBY'S TENSOR FIELDS FOR ARBITRARY DOMAIN: IRREDUCIBLE STRUCTURE, SYMMETRY AND AVERAGE
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ESHELBY'S TENSOR FIELDS FOR ARBITRARY DOMAIN: IRREDUCIBLE STRUCTURE, SYMMETRY AND AVERAGE

机译：eShelby的任意域的张力字段：不可缩小的结构，对称性和平均水平

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This paper reviews some recent theoretical findings relevant to Eshelby tensor fields. The strain field e{sup}ω(x) in an infinitely large, homogenous and isotropic elastic medium induced by a uniform eigenstrain e{sup}0 in a domain ω depends linearly upon e{sup}0. It has been a long-standing conjecture that the Eshelby's tensor field S{sup}ω(x) is uniform inside ω if and only if ω is ellipsoidally shaped. S{sup}ω(x) might have a maximum of 36/9 independent components in three/two dimensions, thanks to its own minor index symmetrical property: (S{sub}(ijkl)){sup}ω=(S{sub}((jikl)){sup}ω=(S{sub}(ijlk)){sup}ω. Making use of the irreducible decomposition of S{sup}ω, we show that the isotropic part S of S{sup}ω is null outside ω and is uniform inside ω with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domain. Further, we show that the anisotropic part A{sup}ω= S{sup}ω -S of S{sup}ωis characterized by a second- and a fourth-order deviatoric tensors and thus contains at maximum 14 or 4 independent components, which characterize the geometry of the domain, in three or two dimensions, respectively. Remarkably, the above irreducible structure of S{sup}ω is independent of ω's geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, et al.). Interestingly, consequences of our results imply a number of recently finding, for example, both the values of S{sup}ω at the center of a 2D C{sub}n(n≥3, n≠4)-symmetric or 3D icosahedral ω and the average value of S{sup}ω over such a ω are equal to S{sup}0.
机译：本文评论了一些与eShelby张磁场相关的一些理论发现。在域ω中由均匀的特征e {sup} 0引起的无限大，均匀的和各向同性弹性介质中的应变场e {sup}ω（x）在e {sup} 0上线性取决于线性。它已经是一个长期猜想，即eShelby的张量场S {sup}ω（x）内部Ω内部均匀，如果ω是椭圆形状的，则才有Ω。 s {sup}ω（x）可能在三​​个/二维中最多包含36/9个独立组件，得益于自己的次要索引对称属性：（s {sub}（ijkl））{sup}ω=（s {子}（（jikl））{sup}ω=（s {sub}（ijlk））{sup}ω。利用S {sup}ω的不可缩小分解，我们表明s {sup的各向同性部分s }Ω外部Ω内部ω均匀，具有与eShelby的张量S0相同的3D球形或2D圆形域。此外，我们表明各向异性部分A {SUP}ω= S {SUP}ω-Ω S {sup}ωis以第二阶和四阶脱离件张量特征，因此最多包含在最大14或4个独立组件，其在三个或两个维度中表征域的几何形状。值得注意的是，上述不可缩小的结构s {sup}ω是独立于ω的几何形状（例如，形状，方向，连接度，凸性，边界光滑度等）。有趣的是，我们的结果的后果意味着许多最近发现，例如，既有价值在2D C {sub} n（n≥3，n≥4）的中心的s {sup}ω的ω和在这种ω上的s {sup}ω的平均值等于s {sup} 0。

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