Surface morphology plays a crucial role in friction between two contacting geomaterial surfaces, yet many questions remain unanswered regarding how detailed frictional responses deviate from analytical solutions for smooth surfaces due to the presence of roughness. In this study, we revisit the Cattaneo-Mindlin problem for contacts between two fractally rough elastic or elasto-plastic spheres generated based on ultra-high degree (e.g., up to 2,000) spherical harmonics with the corresponding wavelength less than a thousandth of the mean grain diameter. Transverse contacts are simulated by finite element method, validated by the extended Cattaneo-Mindlin solution to full slide regime for smooth sphere contacts. Extensive simulations are conducted to study contacts between two rough spheres with various surface geometries, micro friction coefficients, normal contact distances, relative roughness, fractal dimensions, and wavelength ranges. Out results indicate that: (a) the new analytical solution can approximately predict the macro contact response except for extremely high relative roughness and narrow wavelength range; (b) deviations induced by roughness from smooth sphere contacts can be neutralized by plasticity, high normal contact interference, and high micro friction coefficient; and (c) fractal dimension impacts frictional contacts less than relative roughness. The main cause of these phenomena can be credited to the underlying microscale contact information. Contact area and stress distributions and their evolutions provide concrete evidence of these observed behavior. This work provides a pathway for applying computational contact mechanics to many geophysical fields, such as the asperity model in earthquake science and the mechanics of granular materials.

中文翻译：

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具有分形形态的粗糙晶粒之间的摩擦接触


表面形态在两个接触的地质材料表面之间的摩擦中起着至关重要的作用，但关于由于粗糙度的存在，详细的摩擦响应如何偏离光滑表面的解析解，许多问题仍未得到解答。在这项研究中，我们重新审视了两个基于超高度（例如，高达 2,000）球谐波产生的分形粗糙弹性或弹塑性球体之间的接触的 Cattaneo-Mindlin 问题，相应波长小于平均晶粒直径的千分之一。横向接触通过有限元方法进行模拟，并通过扩展的 Cattaneo-Mindlin 解决方案验证为平滑球体接触的全滑动状态。进行了广泛的模拟，以研究具有不同表面几何形状、微摩擦系数、法向接触距离、相对粗糙度、分形尺寸和波长范围的两个粗糙球体之间的接触。结果表明：（a） 除了极高的相对粗糙度和较窄的波长范围外，新的解析解可以近似预测宏接触响应;（b） 光滑球体接触的粗糙度引起的偏差可以通过塑性、高法向接触干涉和高微摩擦系数来抵消;（c） 分形维数对摩擦接触的影响小于相对粗糙度。这些现象的主要原因可以归功于潜在的微观联系信息。接触面积和应力分布及其演变为这些观察到的行为提供了具体证据。这项工作为将计算接触力学应用于许多地球物理领域提供了一条途径，例如地震科学中的凹凸模型和颗粒材料的力学。