APPLICATION OF THE ARBITRARY LAGRANGIAN EULERIAN FORMULATION TO THE NUMERICAL SIMULATION OF STATIONARY FORMING PROCESSES WITH DOMINANT TANGENTIAL MATERIAL MOTION

In this paper, an Arbitrary Lagrangian Eulerian (ALE) formulation has been developed for 3D FEM simulations of quasi-stationary metal forming processes (such as drawing, rolling, extrusion ...). In such a formulation, the mesh is updated independently from the material motion, allowing the mesh to be continuously optimized. It is however difficult in 3D to relocate mesh nodes such that the movement of the material domain boundaries can be followed. In general, it is achieved by setting the normal component of the mesh velocity equal to the normal component of the material velocity for each boundary node. This initial choice was found unsatisfactory for processes with dominant tangential velocity. For such cases, a new procedure has been implemented in the FORGE3 (R) software [1]. The surface nodes are projected onto the intermediate surface computed at the end of the Lagrangian virtual updating stage. Different strategies are developed to project the nodes, according to the topological entities they belong to (vertices, edges, plane or curved surfaces). A comparison for wire and bar drawing processes is provided between a standard Updated Lagrangian formulation [1] and the present ALE formulation, showing very similar results (geometry shape, drawing stress, strain rates ...).