Eshelby Tensor for an Elastic Inclusion With Slightly Weakened Interface
Eshelby Tensor for an Elastic Inclusion With Slightly Weakened Interface
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DOI：
10.1115/1.2900974
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发表时间：
1993-12
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影响因子：
--
通讯作者：
J. Qu
中科院分区：
文献类型：
--
作者：
J. Qu
本文研究无限大弹性矩阵中椭球夹杂的Eshelby张量。夹杂物和基体之间的界面用厚度为零的弹簧层来模拟，而不是假设夹杂物和基体之间的完美结合。如果弹簧层的柔度远小于基体材料的柔度，则可以说夹杂物-基体界面略有减弱。利用线弹性力学中的Betti-Rayleigh互易恒等式，导出了含弹性层界面弹性夹杂位移场的积分表达式。从积分表示出发，通过迭代方法得到了具有弱界面椭球夹杂的Eshelby张量的显式表达式。
The Eshelby tensor for an ellipsoidal inclusion in an elastic matrix of infinite extent is considered in this paper. Instead of assuming perfect bonding between the inclusion and the matrix, the interface between the inclusion and the matrix is modeled by a spring layer of vanishing thickness. The inclusion- matrix interface is said to be slightly weakened if the compliance of the spring layer is much smaller than that of the matrix material. By virtue of the Betti-Rayleigh reciprocal identity in linear elasticity, an integral representation for the displacement field due to an elastic inclusion with a spring layer interface is derived. Explicit expressions of the Eshelby tensor for an ellipsoidal inclusion with slightly weakened interface are obtained through an iteration procedure developed from the integral representation.