Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress
Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress
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DOI：
10.1080/14786435.2013.780668
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发表时间：
2013-07
影响因子：
1.6
通讯作者：
W. Ye;B. Paliwal;A. Ougazzaden;M. Cherkaoui
中科院分区：
文献类型：
--
作者：
W. Ye;B. Paliwal;A. Ougazzaden;M. Cherkaoui
采用本征应变的概念，导出了考虑表面应力的三维各向异性含一般缺陷固体弹性场的一般解析框架。该公式表明，弹性常数和表面的几何特征对确定固体的弹性场起着重要作用。作为应用，得到了无限各向同性圆形纳米线应力场的解析解。并与经典解和复变法的应力场进行了比较。本工作的应力场显示了纳米线尺寸缩小时表面应力的影响，但在宏观尺度上可以忽略不计。与复变量法的幂级数解相比，本文的解析解提供了更好的平台，在各种应用中更加灵活。更重要的是，所提出的分析框架深刻地改进了具有表面效应的一般三维各向异性材料的研究。
The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.