A mixed Eulerian–Lagrangian method for modelling metal extrusion processes

A mixed Eulerian–Lagrangian approach for the computational modelling of metal extrusion processes in complex three dimensional geometries is presented. The approach involves the representation of the workpiece as a pseudo-fluid, and requires the solution of non-Newtonian fluid flow equations in an Eulerian context, using a free-surface algorithm to track its extreme deformation during its extrusion. The solid mechanics equations associated with the tools are solved in a conventional Lagrangian context. Thermal interactions between the workpiece and tools are modelled and a fluid–structure interaction technique is employed to capture the effect of the fluid traction load imposed by the workpiece on the tools, and especially the subsequent adaption of the Eulerian mesh to account for the impact of die deformation. Two extrusion test cases are investigated and the results obtained show the potential of the model with regard to representing the physics of the process, the advantages of the model over a more loosely coupled approach, and the parallel scalability of the resulting software.