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This work proposes a novel model and numerical formulation for lubricatedcontact problems describing the mutual interaction between two deformable 3Dsolid bodies and an interposed fluid film. The solid bodies are consistentlydescribed based on nonlinear continuum mechanics allowing for finitedeformations and arbitrary constitutive laws. The fluid film is modelled as aquasi-2D flow problem on the interface between the solids governed by theaveraged Reynolds equation. The averaged Reynolds equation accounts for surfaceroughness utilizing spatially homogenized, effective fluid parameters and forcavitation through a positivity constraint imposed on the pressure field. Incontrast to existing approaches, the proposed model accounts for theco-existence of frictional contact tractions and hydrodynamic fluid tractionsat every local point on the contact surface of the interacting bodies andcovers the entire range from boundary lubrication to mixed, elastohydrodynamic,and eventually to full film hydrodynamic lubrication in one unified modellingframework with smooth transition between these different regimes. Critically,the model relies on a recently proposed regularization scheme for themechanical contact constraint combining the advantages of classical penalty andLagrange multiplier approaches by expressing the mechanical contact pressure asa function of the effective gap between the solid bodies while at the same timelimiting the minimal gap value occurring at the (theoretical) limit ofinfinitely high contact pressures. From a physical point of view, this approachcan be considered as a model for the elastic deformation of surface asperities,with a bounded magnitude depending on the interacting solids' surfaceroughness. A consistent and accurate model behavior is demonstrated andvalidated by employing several challenging and practically relevant benchmarktest cases.

A Mortar Finite Element Formulation for Large Deformation Lubricated  Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic  and Full Hydrodynamic Lubrication