Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model

Guy Bayada (1, 2, 3) , Sébastien Martin (1) , Carlos Vazquez (4)

1 ICJ - Institut Camille Jordan
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
3 TMI - Tribologie et Mécanique des Interfaces
4 DEP. MATEMATICAS (UNIVERSIDADE A CORUÑA) - Dep. Matematicas (Universidade A Coruña)

The present paper deals with the homogenization of a lubrication problem, using two-scale convergence techniques and periodic unfolding methods. We study in particular the Reynolds-Hertz model, which takes into account elastohydrodynamic deformations of the upper surface, when highly oscillating roughness effects occur. The difficulty arises when considering cavitation free boundary phenomena, leading to highly nonlinear and nonlocal problems.

Mots clés: numerical simulation.; two-scale convergence; numerical simulation; Elastohydrodynamic lubrication; piezoviscous fluid; Elrod-Adams model; homogenization

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Guy Bayada, Sébastien Martin, Carlos Vazquez. Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model. 2004. ⟨hal-00008081v2⟩