Three-dimensional finite element analysis for the industrial extrusion processes using mismatching refinement with domain decomposition

Abstract

Extrusion is a forming process in which a billet is forced to flow through a profiled die. The traditional design procedure for extrusion has mainly depended on the experience and the knowledge of designers and the trial-and-error method, which spends much time and cost. In order to save such consumption, numerical analyses have been implemented to simulate the metal forming processes. The finite element method has been one of the most widely used numerical methods for simulation of various engineering problems including the extrusion process. The three-dimensional finite element analysis of extrusion processes, however, requires large computation time due to its nonlinear characteristics. It is more severe in the extrusion process with thin-walled sections, which needs large degree of freedom for the proper description. In the present study, mismatching refinement is developed with domain decomposition for economic computation of extrusion processes. Mismatching refinement is an efficient domain decomposition method with different mesh densities for several subdomains. The solution is obtained by iterative calculation between subdomains which have different mesh densities. For the convergence of the iterative calculation between subdomains with different mesh densities, various velocity alternating schemes have been proposed and compared. Improvement of convergence has been obtained through the proposed alternating scheme for the mismatching refinement with domain decomposition. Through several numerical examples of the extrusion processes, such as a rectangular section and an ``E``-section, the validity of the proposed method has been demonstrated. The effect of the outlet position has also been investigated through the analysis. The results have revealed that computational efficiency is highly increased, especially for the three-dimensional problems. As a numerical example for hollow section extrusion using a porthole die, an extrusion of a triply-connected ...