  This work proposes a novel model and numerical formulation for lubricated
contact problems describing the mutual interaction between two deformable 3D
solid bodies and an interposed fluid film. The solid bodies are consistently
described based on nonlinear continuum mechanics allowing for finite
deformations and arbitrary constitutive laws. The fluid film is modelled as a
quasi-2D flow problem on the interface between the solids governed by the
averaged Reynolds equation. The averaged Reynolds equation accounts for surface
roughness utilizing spatially homogenized, effective fluid parameters and for
cavitation through a positivity constraint imposed on the pressure field. In
contrast to existing approaches, the proposed model accounts for the
co-existence of frictional contact tractions and hydrodynamic fluid tractions
at every local point on the contact surface of the interacting bodies and
covers the entire range from boundary lubrication to mixed, elastohydrodynamic,
and eventually to full film hydrodynamic lubrication in one unified modelling
framework with smooth transition between these different regimes. Critically,
the model relies on a recently proposed regularization scheme for the
mechanical contact constraint combining the advantages of classical penalty and
Lagrange multiplier approaches by expressing the mechanical contact pressure as
a function of the effective gap between the solid bodies while at the same time
limiting the minimal gap value occurring at the (theoretical) limit of
infinitely high contact pressures. From a physical point of view, this approach
can be considered as a model for the elastic deformation of surface asperities,
with a bounded magnitude depending on the interacting solids' surface
roughness. A consistent and accurate model behavior is demonstrated and
validated by employing several challenging and practically relevant benchmark
test cases.
