Application of ALE finite elements method to a lubricated friction model in sheet metal forming

An Arbitrary Lagrangian Eulerian (ALE) formulation involving the use of an operator splitting procedure is presented. In solid mechanics applications, ALE formulation is employed to overcome mesh distorsion problems in finite deformation. Here, we present a new application to fluid/structure interaction problems: determining the film thickness h in lubricated contact analysis using a method of characteristic in the framework of a finite element method. Hydrodynamic and elastohydrodynamic lubrication regimens are analyzed using an averaged Reynolds equation. The friction stress is then expressed in terms of lubricant parameters such as the film thickness and viscosity and forming process parameters such as the pressure, forming speed and surface roughness. The efficiency of the method is illustrated in the case of three examples. The first one involves the ALE formulation developed here in sheet metal forming and the others are applications to lubricated contact analysis.