# A framework for the analysis of fully coupled normal and tangential contact problems with complex interfaces

arXiv: https://arxiv.org/abs/2110.07932 · HTML: https://mlsanity.com/paper/2110.07932/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Data-Driven Surrogate Modeling Techniques to Predict the Effective Contact Area of Rough Surface Contact Problems](https://mlsanity.com/paper/2504.17354/) (2025)

## Abstract (arXiv)

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.