An extension to the interface finite element with eMbedded Profile for Joint Roughness (MPJR interface finite element) is herein proposed for solving the frictional contact problem between a rigid indenter of any complex shape and an elastic body under generic oblique load histories. The actual shape of the indenter is accounted for as a correction of the gap function. A regularised version of the Coulomb friction law is employed for modeling the tangential contact response, while a penalty approach is introduced in the normal contact direction. The development of the finite element (FE) formulation stemming from its variational formalism is thoroughly derived and the model is validated in relation to challenging scenarios for standard (alternative) finite element procedures and analytical methods, such as the contact with multi-scale rough profiles. The present framework enables the comprehensive investigation of the system response due to the occurrence of tangential tractions, which are at the origin of important phenomena such as wear and fretting fatigue, together with the analysis of the effects of coupling between normal and tangential contact tractions. This scenario is herein investigated in relation to challenging physical problems involving arbitrary loading histories.

本文提出了对具有嵌入式接头粗糙度轮廓的界面有限元（MPJR 界面有限元）的扩展，用于解决任何复杂形状的刚性压头与一般倾斜载荷历史下弹性体之间的摩擦接触问题。压头的实际形状被视为间隙函数的修正。库仑摩擦定律的正则化版本用于对切向接触响应进行建模，同时在法向接触方向引入惩罚方法。源自其变分形式主义的有限元 (FE) 公式的发展是彻底推导出来的，并且该模型在标准（替代）有限元程序和分析方法的挑战性场景中得到验证，例如与多尺度粗糙轮廓的接触。本框架能够全面研究由于切向牵引力的发生而引起的系统响应，切向牵引力是磨损和微动疲劳等重要现象的起源，同时分析法向和切向接触牵引力之间的耦合效应。此处针对涉及任意加载历史的具有挑战性的物理问题来研究该场景。