Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity
Elastic field of an isotropic matrix with a nanoscale elliptical inhomogeneity
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DOI：
10.1016/j.ijsolstr.2007.05.019
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发表时间：
2007-12
影响因子：
3.6
通讯作者：
Lian Tian;R. Rajapakse
中科院分区：
文献类型：
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作者：
Lian Tian;R. Rajapakse
在传统的连续介质力学中，表面能的影响被忽略，因为它是小的相比，体能量。然而，对于纳米材料和结构，由于高的表面/体积比，表面效应变得显著。本文研究了无限大基体中纳米尺度椭圆形夹杂在任意远程载荷作用下的二维弹性场，并研究了夹杂中均匀本征应变。Gurtin-Murdoch表面/界面弹性模型被应用到考虑表面/界面应力效应。利用Muskhelishvili的复变技巧，得到了无穷级数形式的解析势函数。选定的数值结果研究的弹性场的尺寸依赖性和表面弹性模量和表面残余应力的影响。研究发现，当考虑界面应力效应时，均匀本征应变下椭圆夹杂的弹性场不再是均匀的。
In traditional continuum mechanics, the effect of surface energy is ignored as it is small compared to the bulk energy. For nanoscale materials and structures, however, the surface effects become significant due to the high surface/volume ratio. In this paper, two-dimensional elastic field of a nanoscale elliptical inhomogeneity embedded in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin–Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. By using the complex variable technique of Muskhelishvili, the analytic potential functions are obtained in the form of an infinite series. Selected numerical results are presented to study the size-dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. It is found that the elastic field of an elliptic inhomogeneity under uniform eigenstrain is no longer uniform when the interfacial stress effects are taken into account.