降维方法的有效性：接触面积、平均界面分离和接触刚度
On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness
摘要：
最近有人建议，许多固体之间的接触力学问题可以通过映射到一个有效的一维（1D）弹性地基模型的问题，准确地研究。使用这个一维映射，我们计算的接触面积和平均界面分离的弹性固体与名义上平坦，但随机粗糙的表面。我们表明，通过比较精确的数值结果，一维映射方法失败，甚至定性。我们还计算了正常的界面刚度$K$，并将其与分析研究的结果进行了比较。我们将弹性地基模型的失效归因于忽略了微凸体接触区域之间的长程弹性耦合。
英文摘要：
It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness $K$ and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions.
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