The elastic loading behaviour of rough surfaces is derived based on the physical understanding of the contact phenomena, where the pressure distribution is analytically obtained without any negative values or convergence problems, thus the evolution of the contact behaviour is obtained in a semi-analytical manner. Numerical results obtained by the proposed approach facilitate the understanding of the contact behaviour in the following aspects: 1) the ratio of contact area to load decreases with an increase in real contact area; 2) normal approach-load relationship is approximated by an exponential decay under relatively small loads and a linear decay under relatively large loads; and 3) average gap shows an exponential relationship with load only in moderate load range.

中文翻译：

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粗糙表面弹性加载行为的半解析方法

粗糙表面的弹性加载行为是基于对接触现象的物理理解而得出的，其中通过分析获得压力分布而没有任何负值或收敛问题，因此以半解析方式获得了接触行为的演变。通过所提出的方法获得的数值结果有助于从以下方面理解接触行为：1）接触面积与负载的比率随着实际接触面积的增加而减小；2）正常的进场-负荷关系通过较小负荷下的指数衰减和较大负荷下的线性衰减来近似。3）平均间隙仅在中等载荷范围内与载荷呈指数关系。