物質的尺度越小，其表面積對體積之比例越大，表面效應愈大。廣義上，固體的表面應力不像流體之表面張力，具有等向特性；而固體之表面/界面應力是具有方向性的，這與固體表面的結晶方向存在有關係。本文擬以簡單直觀的方式，重新推導描述固體界面情況的廣義Young-Laplace方程式，以建立固體表面應力或界面應力在巨觀行為的架構；同時以相同的方式，推導熱傳導的界面模型，期望在表面/界面應力相關的實際問題中，提供一個簡便而直觀的程序。另外本文也以能量法架構球形和圓柱形異向性內含物在不同變形模式下固體界面的數學模式。

The significance of surfaces becomes important in nano-scale structures in which the surface to volume ratio is high. In contrast with fluids, surface/interface stresses in solids may depend on crystallographic parameters and are generally non-hydrostatic. The interface conditions between two different solids incorporating the interface stresses will be referred to as the “generalized Young-Laplace equation”. In order to obtain a better understanding of the physical meaning of the generalized Young-Laplace equation, here we present a different derivation. The idea is based on the notion that the interface stresses can be modeled as in-plane stresses along the tangent planes of the curved surface and the stress vectors on the top and bottom of the curved surfaces are taken from its three-dimensional bulk neighborhood. Similar procedures can be applied to conduction phenomena. On the other hand, energy approach could be an alternative method to construct the interface condition. We will adopt this method to formulate the interface conditions for spherical and cylindrical inclusions.

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