Due to the large surface/interface-to-volume ratio, surface/interface effect in nanomaterials begins to play an important role in changing the constitutive law seen in classical elasticity theory. This work investigates the size-dependent elastic field of nano-inhomogeneity due to interface and interphase effect, respectively. Closed-form solution to the elastic field of nano-inhomogeneity with interface and interphase effect is found. For comparison, the numerical result of InAs/GaAs system is provided as an example, which demonstrates that interface and interphase effect could have significant influence on the elastic field of nano-inhomogeneity. The continuity/discontinuity of the elastic field of nano-inhomogeneity with interface and interphase effect is discussed in detail. It is verified both numerically and analytically that the elastic field from interphase effect tends to converge to that from interface effect when the interphase thickness shrinks to zero. Furthermore, all results converge to the classical solution at positions far away from the interfacial region, so it is unnecessary to distinguish interface or interphase effect at positions far away from the interfacial region in practical situations.

中文翻译：

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纳米非均匀性的尺寸依赖性弹性场：从界面效应到相间效应

由于较大的表面/界面体积比，纳米材料中的表面/界面效应开始在改变经典弹性理论中的本构律方面起重要作用。这项工作分别研究了由于界面和相间效应而导致的纳米非均匀性的尺寸依赖性弹性场。找到了具有界面和相间效应的纳米非均匀弹性场的封闭形式解。为了进行比较，以InAs / GaAs系统的数值结果为例，表明界面和相间效应可能对纳米非均匀性的弹性场产生重大影响。详细讨论了具有界面和相间效应的纳米非均匀性弹性场的连续性/不连续性。数值和分析都证明，当相间厚度减小到零时，相间作用的弹性场趋于收敛于界面作用的弹性场。此外，所有结果都在远离界面区域的位置收敛到经典解，因此在实际情况下没有必要在远离界面区域的位置上区分界面或界面效应。