A mortar-finite element approach to lubricated contact problems

In this paper, a new numerical approach, based on mortar discretization of interface fields, is proposed to solve lubricated contact problems between deformable solid bodies. The Reynolds approximation to the thin film fluid equations is used to describe the fluid behavior on the interface, while the equations of small strain elasticity (to which finite elements are applied) are assumed to govern the solid body behavior. The result of this approach is a monolithic scheme in which the fluid and solid mechanics are solved simultaneously, without the need for iterative or staggered approaches between the fluid and solid phases. atures of the approach are that the fluid film thickness, directly related to the deformation of the solid phase, is computed from a least squares projection based on dual basis functions (as pioneered by Wohlmuth [B.I. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition, Springer-Verlag, Heidelberg, 2001]). The free boundary problem for the fluid phase, corresponding to the boundary between lubricated and cavitated regions, is regularized with a penalty method and thus resolved as part of the solution. Several numerical examples are given to demonstrate the approach.