On a variational inequality on elasto-hydrodynamic lubrication

Abstract

We consider the problem of a deformable surface moving over a flat plane. The surfaces are separated by a small gap filled by a lubricant fluid. The mathematical model consists of the Reynolds variational inequality with nonlocal coefficients given by an integral operator which depends on the fluid pressure. The nonlocal operator represents the deformation of the lubricated surfaces. The problem considers the vertical displacement of the elastic surface from its reference configuration. The goal of the paper is to obtain the range of these admissible displacements. We present general results for nonlocal coefficients with applications to particular problems in elasto-hydrodynamic lubrication.