Contact and friction interactions play an essential role in many quotidian contexts, including those related to industry (e.g., tire-road and wheel-rail contacts, electric switches, bearings, and brake systems), everyday human activity (e.g., walking, handling, touching, and sitting) and natural phenomena (e.g., earthquakes, landslides, and glacier motion). Regardless of such prevalence, contact-related mechanisms (friction, adhesion, and wear) are still not fully understood and thus are among the most cutting edge research topics in the mechanical community.

Numerous models of contact-related mechanisms exist at structural scale. They serve to model interfacial normal and tangential stiffness, frictional resistance, material removal on rubbing surfaces (wear), heat transfer between contacting solids, contact electric resistance, adhesion, interfacial fluid flow, microstructural changes in near-contact material layers, fretting life-cycle, debris generation, lubrication, especially in mixed regime, and other mechanisms. Admittedly, all the aforementioned phenomena are strongly related to the surface roughness. The associated models can be incorporated in a macroscopic/structural model via constitutive interfacial equations. These equations can be based either on experimental data, and thus remain purely phenomenological, or can take the microscopic roughness as the starting point.

The latter class of models shall have a greater predictive power, and potentially can be used for a large spectrum of applications. However, because of the strong non-linearity of the contact/friction mechanisms and extreme complexity of surface roughness, construction of a reliable analytical micro-mechanical model presents a serious challenge.

In this work, we present recent results in modelling and simulation of mechanical and multi-field aspects of the “rough contact”. First, we present a technique to determine accurately the true contact area in the framework of a spectral boundary element method used to solve the contact between two rough surface [1,2]. This technique enables us to uncover a subtle link between the so-called Nayak parameter and the rate of the contact area growth with the applied squeezing pressure [3]. Apart from studying the growth of the true contact area, we study how the presence of a fluid (compressible and incompressible) in the contact interface affects the contact characteristics. Moreover, an interplay of solid contact and fluid flow as well as an entrapment of the latter are considered. Two different approaches are used to handle this problem. The first one assumes a one-way weak coupling between the solid deformation and the fluid flow. This approach uses the already mentioned spectral-based boundary element method [1] to solve the non-linear contact problem in the context of infinitesimal deformations, a separate finite element solver is used to solve a viscous laminar fluid flow through the opening in the contact interface, which is governed by Reynolds equation. A second approach, assumes a strong coupling between fluid and solid equations. Within this approach both equations are solved simultaneously within a monolithic and strongly coupled framework implemented using the finite element method. Some model problems of fluid entrapment and flow through a wavy channel assuming strong coupling of equations are presented [4,5]. An engineering study of a fluid flow in contact interface between elasto-plastic solids at roughness scale will be also discussed.

References

[1] H.M. Stanley, T. Kato. Journal of Tribology ASME, 119:481-485 (1997).

[2] V.A. Yastrebov, G. Anciaux, J.F. Molinari.Tribology International, 114:161-171 (2017).

[3] V.A. Yastrebov, G. Anciaux, J.F. Molinari. Journal of the Mechanics and Physics of Solids, 107:469-493 (2017).

[4] A.G. Shvarts, V.A. Yastrebov. Tribology International, 126:116-126 (2018).

[5] A.G. Shvarts, V.A. Yastrebov. Journal of the Mechanics and Physics of Solids, 119:140-162 (2018).