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首页> 外文期刊>Journal of thermal stresses >THE PROOF OF STRAIN DISCONTINUITY IN ESHELBY PROBLEMS WITH ROTATIONAL SYMMETRICAL INCLUSIONS
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THE PROOF OF STRAIN DISCONTINUITY IN ESHELBY PROBLEMS WITH ROTATIONAL SYMMETRICAL INCLUSIONS

机译：旋转对称包含在Eshelby问题中应变不连续性的证明

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摘要

One of the important approaches to study thermal stress in heterogeneous materialldevices is the Eshelby equivalent inclusion method, which is based on the Eshelby uniform solution (the Eshelby property) for ellipsoid-like inclusions. Despite the non-uniformity in stresses fields, it has been proved [11] that rotational symmetrical inclusions satisfy the arithmetic mean theorem (the quasi-Eshelby property). That is, for N-fold rotational symmetric inclusions, the average (more accurately, the arithmetic mean) of the strains inside the inclusion equals the strain of the circular inclusion and vanishes for the points outside the inclusion. Similar to the Eshelby property, the quasi-Eshelby property can be used to study induced internal stress in micromechanics via the Eshelby equivalent inclusion method. Consequently, the Eshelby equivalent inclusion method can be extended to study inclusions of rotational symmetrical shape. In this paper, the discontinuity relation of the average strains in the Eshelby problem of rotational symmetrical inclusions obtained by [11] is proved by virtue of the stress continuity and the discontinuity of the displacement gradient.
机译：研究异质材料器件中热应力的重要方法之一是Eshelby等效夹杂物法，它基于椭球状夹杂物的Eshelby均匀溶液（Eshelby性质）。尽管应力场不均匀，但已证明[11]，旋转对称夹杂物满足算术平均定理（准Eshelby性质）。也就是说，对于N倍旋转对称夹杂物，夹杂物内部的应变的平均值（更准确地说是算术平均值）等于圆形夹杂物的应变，并且对于夹杂物外部的点消失。与Eshelby属性相似，准Eshelby属性可用于通过Eshelby等效夹杂法研究微机械中的内部应力。因此，Eshelby等效夹杂物方法可以扩展到研究旋转对称形状的夹杂物。在本文中，通过应力连续性和位移梯度的不连续性，证明了[11]获得的旋转对称夹杂物的Eshelby问题中平均应变的不连续性。

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