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

TL;DR

This work extends the MPJR interface finite element to address fully coupled normal and tangential frictional contact with complicated rough interfaces by embedding the actual rough geometry as a gap correction on a nominally smooth interface. The approach combines a normal penalty and a regularised Coulomb friction law within a variational framework and introduces a zero-thickness composite interface that maps a two-body problem to an equivalent rigid-indenter/elastic-half-plane formulation. The MPJR interface element discretizes the interface with four nodes while storing roughness analytically, enabling efficient meshing and robust convergence for multi-scale rough profiles. Validation against Hertzian-like benchmarks and Weierstrass-profile scenarios demonstrates accurate coupling effects, reduced mesh complexity, and applicability to oblique loading histories. The method provides a practical tool for analyzing wear, fretting fatigue, and the interaction of rough surfaces under complex loading, with clear paths to three-dimensional extensions and broader friction law formulations.

Abstract

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.

Figures (16)

• Figure 1: domains $\Omega_i$$(i=1,2)$, their Dirichlet $(\partial\Omega_i^D)$ and Neumann $(\partial\Omega_i^N)$ boundaries, and the contact interface $\partial\mathcal{B}_\mathrm{C}$.
• Figure 2: Composite topography of the interface embedding a rough profile
• Figure 3: Zero-thickness interface model defining the equivalent interface $\partial \mathcal{B}_\mathrm{C}^\ast$.
• Figure 4: Parametrisation of two rough profiles composing an interface $\Gamma_\mathrm{C}$.
• Figure 5: FEM approximation of the interface.