Finite element simulation of lubricated contact in rolling using the arbitrary Lagrangian–Eulerian formulation Original Research Article

In this paper, the lubrication problem in numerical simulation of forming processes is considered. Two efficient convection algorithms are presented in order to update the value stored at the Gauss points during the Eulerian step of an arbitrary Lagrangian Eulerian computation in solid mechanics. They are based on the finite volume method and on the streamline upwind Petrov Galerkin method. After enumerating the difficulties encountered when trying to solve the lubrication problem with the finite element method, a generalization of the formulation introduced by Liu [Simulation of Ring Rolling Process by Arbitrary Lagrangian Eulerian Finite Element Method, vol. 20, p. 225; ASME Winter Meeting, Dallas, Tx, 1990, Int. J. Numer. Methods Engrg. 36 (1993) 855; Numerical Methods in Industrial Forming Processes, Valbonne, France, 1992, p. 731] for the thin film hydrodynamic lubrication regime is presented. This method is then applied to a strip rolling simulation, using the arbitrary Lagrangian Eulerian formalism.