Hamburg University of Technology, Department of Mechanical Engineering, Am Schwarzenberg-Campus 1, 21073, Hamburg, Germany.
Imperial College London, Exhibition Road, London, SW7 2AZ, UK.
Sci Rep. 2017 Jul 31;7(1):6900. doi: 10.1038/s41598-017-07234-4.
There are two main approximate theories in the contact of rough solids: Greenwood-Williamson asperity theories (GW) and Persson theories. Neither of them has been fully assessed so far with respect to load-separation curves. Focusing on the most important case of low fractal dimension (D = 2.2) with extensive numerical studies we find that: (i) Persson's theory describes well the regime of intermediate pressures/contact area, but requires significant corrective factors: the latter depend also on upper wavevector cutoff of the roughness; hence, (ii) Persson's theory does not predict the correct functional dependence on magnification; (iii) asperity theories in the discrete version even neglecting interaction effects are more appropriate in the range of relatively large separations, also to take into consideration of the large scatter in actual realization of the surface.
目前，粗糙固体接触的理论主要有两种：Greenwood-Williamson 粗糙峰理论（GW）和 Persson 理论。迄今为止，还没有对这两种理论进行关于载荷-分离曲线的全面评估。通过对最重要的低分形维数（D=2.2）情况进行广泛的数值研究，我们发现：（i）Persson 理论能够很好地描述中等压力/接触面积的区域，但需要进行显著的修正，修正系数也取决于粗糙度的上波矢量截止值；因此，（ii）Persson 理论并不能预测出与放大倍数的正确函数关系；（iii）即使忽略了离散形式的粗糙峰理论中的相互作用效应，在相对较大的分离范围内，该理论也更为适用，这也考虑到了表面实际实现中的大离散性。
