A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.

中文翻译：

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粗糙表面间接触力学的多尺度 FEM-BEM 公式

本文提出了一种用于名义上光滑但微观上粗糙的表面之间的接触力学的新型多尺度有限元公式。该方法将用于在宏观尺度上模拟界面相互作用的界面有限元法 (FEM) 与用于求解微观尺度接触问题的边界元法 (BEM) 相结合。在每个积分点使用边界元法来确定法向接触牵引力和法向接触刚度，允许考虑任何理想的粗糙拓扑，无论是真实的，例如从轮廓数据中获得的，还是人工的，用最合适的数值进行评估或分析方法。结合选定的基准测试讨论了加速 FEM 和 BEM 之间耦合的不同数值策略。