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首页> 外文期刊>Philosophical Magazine Letters >Averaged Eshelby tensor and elastic strain energy of a superspherical inclusion with uniform eigenstrains
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Averaged Eshelby tensor and elastic strain energy of a superspherical inclusion with uniform eigenstrains

机译：具有均匀特征应变的超球形夹杂物的平​​均Eshelby张量和弹性应变能

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摘要

A shape described by (x_1~2)~(p/2) + (x_2~2)~(p/2) + (x_3~2)~(p/2) ≤ 1 (p ≥ 2) may be called a supersphere. This shape becomes a sphere and a cuboid when p = 2 and p → ∞ respectively. Shape changes of some precipitates in solid materials are well approximated by the variation in p of the supersphere. Here the elastic states of an infinitely extended material containing a superspherical inclusion Ω with uniform eigenstrains are examined. A case where Ω has the same isotropic elastic moduli as those of the remainder is treated. The averaged Eshelby tensor of the superspherical Ω is calculated as a function of p. Using the elastic strain energy of the material containing the superspherical Ω and its change with transitions of the Ω shape from spherical to cuboidal are discussed.
机译：由（x_1〜2）〜（p / 2）+（x_2〜2）〜（p / 2）+（x_3〜2）〜（p / 2）≤1（p≥2）描述的形状可以称为超球。当p = 2和p→∞时，此形状分别变为球体和长方体。固体材料中某些沉淀物的形状变化可以通过超球体p的变化很好地估算出来。在此，检查了具有均匀特征应变的包含超球形夹杂物Ω的无限延伸材料的弹性状态。处理其中Ω具有与其余部分相同的各向同性弹性模量的情况。计算超球面Ω的平均Eshelby张量作为p的函数。使用讨论了包含超球形Ω的材料的弹性应变能及其随Ω形状从球形过渡到长方体的变化。

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