Explicit expression of Eshelby tensor for arbitrary weakly non-circular inclusion in two-dimensional elasticity
Explicit expression of Eshelby tensor for arbitrary weakly non-circular inclusion in two-dimensional elasticity
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DOI：
10.1016/j.ijengsci.2009.01.005
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发表时间：
2009-11
影响因子：
6.6
通讯作者：
Mojia Huang;W. Zou;Q. Zheng
中科院分区：
文献类型：
--
作者：
Mojia Huang;W. Zou;Q. Zheng
椭球包体在无限弹性介质中的任何恒定特征应变都会导致包体中的应变场和应力场均匀，称为Eshelby均匀性。表征Eshelby均匀性的Eshelby张量在基粒复合材料细观力学中起着至关重要的作用。由于Eshelby均匀性对任何非椭球包涵都不成立，且没有非椭球包涵的通解，本文利用傅里叶级数对二维各向同性弹性中弱非圆包涵的形状进行了表征，得到了其Eshelby张量的显式表达式。进一步给出了包含上平均Eshelby张量的表达式。平均Eshelby张量只取决于傅里叶级数的二阶和四阶系数。最后，我们将这些表达式的计算结果与各种弱非圆内含物的精确数值结果进行了比较，验证了这些表达式。
Any constant eigenstrain of an ellipsoidal inclusion in an infinite elastic medium results in uniform strain and stress fields in the inclusion, known as the Eshelby uniformity. The Eshelby tensor which characterizes the Eshelby uniformity plays a crucial role in micromechanics of matrix–particle composites. Since the Eshelby uniformity is not valid for any non-elliposidal inclusion and a general solution for the non-elliposidal inclusion is not available, herein we use the Fourier’s series to characterize the shape of the weakly non-circular inclusion in two-dimensional isotropic elasticity and obtain the explicit expression of its Eshelby tensor. We further give the expression of the average Eshelby tensor on the inclusion. The average Eshelby tensor depends upon only the second- and the fourth-shape coefficients of the Fourier’s series. Finally, we verify these expressions by comparing their computational results with the exact numerical results for various weakly non-circular inclusions.