The relative contact area of rough surface contacts is known to increase linearly with reduced pressure, with proportionality factor \(\kappa\). In its common definition, the reduced pressure contains the root-mean-square gradient (RMSG) of the surface. Although easy to measure, the RMSG of the entire surface does not coincide, at small loads, with the RMSG over the actual contact area \({\bar{g}}_{\text {r}}\), which gives a better description of the contact between rough surfaces. It was recently shown that, for Hertzian contacts, linearity between area and load is indeed obtained only if the RMSG is determined over the actual contact area. Similar to surface contacts, in line contacts, numerical data are often studied using theories that predict linearity by design. In this work, we revisit line contact problems and examine whether or not the assumption of linearity for line contacts holds true. We demonstrate, using Green’s function molecular dynamics simulations, that \(\kappa\) for line contacts is not a constant: It depends on both the reduced pressure and the Hurst exponent. However, linearity holds when the RMSG is measured over the actual contact area. In that case, we could compare \(\kappa\) for line and surface contacts and found that their ratio is approximately 0.9. Finally, by analytically deriving the proportionality factor using \({\bar{g}}_{\text {r}}\) in the original model of Greenwood and Williamson, a value is obtained that is surprisingly in good agreement with our numerical results for rough surface contacts.

中文翻译：

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关于线接触中面积与负载之间的比例。

已知粗糙表面接触的相对接触面积随着压力的减小而线性增加，比例系数为（kappa）。在其通用定义中，减压包含表面的均方根梯度（RMSG）。尽管易于测量，但整个表面的RMSG在小负载下与实际接触区域\（{\ bar {g}} _ {\ text {r}} \\）上的RMSG并不重合，可以更好地描述粗糙表面之间的接触。最近表明，对于赫兹接触，仅当在实际接触面积上确定了RMSG时，面积和负载之间的线性才真正获得。与表面接触类似，在线接触中，经常使用通过设计预测线性的理论来研究数值数据。在这项工作中，我们重新审视了线接触问题，并检验了线接触的线性假设是否成立。我们使用格林函数分子动力学模拟证明，线接触的\（\ kappa \）不是常数：它取决于减压和Hurst指数。但是，当在实际接触面积上测量RMSG时，线性保持不变。在这种情况下，我们可以比较\（\ kappa \）对于线和表面接触，发现它们的比率约为0.9。最后，通过在Greenwood和Williamson的原始模型中使用\（{\ bar {g}} _ {\ text {r}} \）来解析得出比例因子，得出的值令人惊讶地与我们的数值很好地吻合表面粗糙接触的结果。