New development and evaluation of stress analysis in nano-scale domain considering surface stresses

从2002年到2003年，我们进行了题为“考虑表面应力的纳米尺度应力分析的新发展和评价”的研究。我们对考虑表面应力的表面现象进行了一些基本分析。最后，我们可以得到如下结果：在表面应力以阶梯方式变化的各向异性材料中，我们可以推导出应力和位移的简单表达式。利用该表达式，当As、Ge等覆盖在Si表面时，Si表面的键长发生变化，从而可以评价键长变化。用第一性原理计算法对键长变化进行了评价。利用弹性力学理论进行了粘着接触分析。边界条件考虑了由表面能产生的表面应力。用于压头和基材表面。此外，我们还认为，与非粘着区相比，粘着区的表面应力要大得多，并且比原始表面应力要小。将抛物面压头压入基材，并且在所述压头和基材的两个表面之间发生粘附。由于表面应力的变化，压头和基材粘附区域的表面向内变形。这意味着粘附区域之间的吸引力是为了保持区域的接触而产生的，并且需要压头从基材上的拉拔力。精确检测了压头与基体之间的接触压力分布、粘附区域表面轮廓和粘附力。分析结果与赫兹理论的结果进行了比较。根据赫兹理论，压头与基板之间的总力约为无量纲接触载荷的0.04 ~ 0.06。利用弹性理论推导了考虑表面应力的表面格林函数。在此基础上，推导了表面偶极格林函数，并将该理论推导的表面原子位移与MD理论进行了比较。少

We performed the study titled of 'New development and evaluation of stress analysis in nano-scale domain considering surface stresses' from 2002 to 2003. We performed several fundamental analyses on surface phenomena considering surface stresses. Finally, we could get the following results.1.We could derive simple expressions for stresses and displacements in anisotropic materials where surface stresses vary in a step manner. Using this expressions, when As,Ge and so on cover the surface on Si, the bond length at Si surface varies, and then the variation of bond length could be evaluated. The variation of bond length was evaluated using the first principle calculation.2.The adhesion contact analysis using the theory of elasticity was performed. The boundary condition considering the surface stresses, which are originated from surface energy. was employed for the surfaces of indenter and substrate. Furthermore, it was supposed the surface stresses in an adhesion region are different fro … More m that in a non-adhesion region and are reduced from the original surface stresses. A paraboloidal indenter is pressed into the substrate and adhesion occurs between two surfaces of the indenter and the substrate. The surfaces at the adhesion regions of the indenter and the substrate deformed inward due to the variation of the surface stresses. This means that the attractive force between the adhesion region occurs for maintaining the contact of the regions and the pull-off force of the indenter from the substrate is needed. The distribution of contact pressure, the surface profile of adhesion region and adhesive force between the indenter and the substrate were precisely examined. The results in the analysis were compared with those in the Hertz theory. The total force between the indenter and the substrate was about the value of 0.04 to 0.06 reduced from the dimensionless contact load based on Hertz theory.3.Surface Green function considering surface stresses is derived using the theory of elasticity. Furthermore, a surface dipole Green function was derived, and the displacements at the surface atoms deduced from the theory were compared with those from MD. The theory considering surface stresses is useful in a nano scale domain. Less