A homogenized micro-elastohydrodynamic lubrication model: Accounting for non-negligible microscopic quantities

In rough elastohydrodynamic lubricated contacts the geometry often exhibits two clearly separated scales: a macroscopic scale -the one of the bearing- and a microscopic scale, that of the surface roughness. In numerical simulation of lubricated contacts, this difference in scales leads to large systems of equations to solve. Assuming periodicity or pseudo-periodicity of the small scale, several methods to decouple the macro scale from the micro scale have been proposed, the formal approach being the homogenization theory. However, the approximation errors due to the classical asymptotic assumptions can be considerable. In this work we introduce a homogenized model which takes into account the non-negligible pressures and deformations of the micro scale, thus extending the applicability of the classical asymptotic homogenized approaches.