A long-standing debate and challenge in contact mechanics is to confirm the linearity between the real contact area and load on rough surfaces as well as its proportionality. Here, we first theoretically prove the linearity between the real contact area and load on rough surfaces by considering an infinite number of surface asperities. The mechanism for such linearity is that the applied force on each “small region” on the rough surface is directly proportional to the area of the region, resulting in a statistical proportionality between the total load and area. This explanation is confirmed via Green's function molecular dynamics (GFMD) simulations. On this basis, we develop a novel framework of surface slope-based multi-asperity contact model. The proportionality between the contact load and area is governed by the elastic property, mean absolute slope, and shape coefficient of the contact surface over the pressed depth. The elastic contacts of single-scale and multiscale rough surfaces are investigated using the developed contact model and GFMD. The shape coefficient of rough surfaces predicted by numerical simulations closely resembles that of surfaces with symmetric parabolic asperities. This work not only sheds light on the physical mechanism underlying the linearity between the contact area and load on rough surfaces but also provides a theoretical foundation for designing and evaluating surface contact and friction performance in micro- and nano-engineering systems.

中文翻译：

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统一粗糙表面接触中实际接触面积和载荷之间的线性比例


接触力学中一个长期存在的争论和挑战是确认实际接触面积与粗糙表面上的载荷之间的线性度及其比例。在这里，我们首先通过考虑无限数量的表面凹凸，从理论上证明了实际接触面积和粗糙表面上的载荷之间的线性度。这种线性的机制是，施加在粗糙表面上每个“小区域”上的力与该区域的面积成正比，从而产生总载荷和面积之间的统计比例。格林函数分子动力学 （GFMD） 模拟证实了这一解释。在此基础上，我们开发了一种新的基于表面坡度的多凹面接触模型框架。接触载荷和面积之间的比例由接触表面的弹性特性、平均绝对斜率和压制深度上的形状系数决定。使用开发的接触模型和 GFMD 研究了单尺度和多尺度粗糙表面的弹性接触。数值模拟预测的粗糙表面的形状系数与具有对称抛物线凹凸的表面的形状系数非常相似。这项工作不仅阐明了粗糙表面上接触面积和载荷之间线性关系的物理机制，还为设计和评估微纳米工程系统中的表面接触和摩擦性能提供了理论基础。