A new finite element paradigm to solve contact problems with roughness

TL;DR

This paper introduces a novel finite element approach using the MPJR interface element to efficiently simulate complex contact problems involving rough and nonlinear surfaces, including friction and adhesion, in 3D.

Contribution

The paper generalizes the MPJR interface element to handle 3D rough surfaces and nonlinear interface behaviors, enabling more accurate and efficient contact simulations.

Findings

Validated with BEM solutions for linear elastic contact.

Successfully applied to nonlinear contact problems difficult for traditional methods.

Demonstrated potential for advanced tribology simulations.

Abstract

This article's main scope is the presentation of a computational method for the simulation of contact problems within the finite element method involving complex and rough surfaces. The approach relies on the MPJR (eMbedded Profile for Joint Roughness) interface finite element proposed in [arXiv:1805.07207], which is nominally flat but can embed at the nodal level any arbitrary height to reconstruct the displacement field due to contact in the presence of roughness. Here, the formulation is generalized to handle 3D surface height fields and any arbitrary nonlinear interface constitutive relation, including friction and adhesion. The methodology is herein validated with BEM solutions for linear elastic contact problems. Then, a selection of nonlinear contact problems prohibitive to be simulated by BEM and by standard contact algorithms in FEM are detailed, to highlight the promising aspects of the proposed method for tribology.