On the Contact Area and Mean Gap of Rough, Elastic Contacts: Dimensional Analysis, Numerical Corrections, and Reference Data
On the Contact Area and Mean Gap of Rough, Elastic Contacts: Dimensional Analysis, Numerical Corrections, and Reference Data
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DOI：
10.1007/s11249-013-0282-z
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发表时间：
2014-02-01
影响因子：
3.2
通讯作者：
Mueser, Martin H.
中科院分区：
文献类型：
--
作者：
Prodanov, Nikolay;Dapp, Wolf B.;Mueser, Martin H.
描述具有自仿射表面粗糙度的固体之间的弹性、非粘附性接触似乎需要大量参数的知识。然而，正如我们通过量纲分析和数值模拟相结合所表明的那样，很少有参数足以决定许多重要的界面性质。这一观点被用来推导相对接触面积和平均界面分离的压力依赖关系，并以紧凑的形式给出结果。给出了压力p的适当单位选择，即有效模数E(*)乘以均方根梯度，相对接触面积主要取决于p而不是赫斯特指数H，即使在较大的p时，当均方根高度作为长度单位时，还取决于长短波长的高度谱截止值之比。在该比率为零的分维极限中，仅与短波长的粗糙度有关。然而，这一限制不应与实际应用相关。我们的工作包括对所使用的格林函数分子动力学数值方法的简要总结，包括如何通过适当的有限尺寸、分形和离散化校正来系统地克服数值缺陷。此外，我们还概述了Persson理论在无量纲单位中的推导过程。Persson理论与数值参考数据进行了很好的比较。
The description of elastic, nonadhesive contacts between solids with self-affine surface roughness seems to necessitate knowledge of a large number of parameters. However, few parameters suffice to determine many important interfacial properties as we show by combining dimensional analysis with numerical simulations. This insight is used to deduce the pressure dependence of the relative contact area and the mean interfacial separation and to present the results in a compact form. Given a proper unit choice for pressure p, i.e., effective modulus E (*) times the root mean square gradient , the relative contact area mainly depends on p but barely on the Hurst exponent H even at large p. When using the root mean square height as unit of length, additionally depends on the ratio of the height spectrum cutoffs at short and long wavelengths. In the fractal limit, where that ratio is zero, solely the roughness at short wavelengths is relevant for . This limit, however, should not be relevant for practical applications. Our work contains a brief summary of the employed numerical method Green's function molecular dynamics including an illustration of how to systematically overcome numerical shortcomings through appropriate finite-size, fractal, and discretization corrections. Additionally, we outline the derivation of Persson theory in dimensionless units. Persson theory compares well to the numerical reference data.