The ALE-method with triangular elements: direct convection of integration point values

The arbitrary Lagrangian-Eulerian (ALE) finite element method is applied to the simulation of forming processes where material is highly deformed. Her e, the split formulation is used: a Lagrangian step is done with an implici t finite element formulation, followed by an explicit (purely convective) E ulerian step. The purpose of this study is to investigate the Eulerian step for quadratic triangular elements. To solve the convection equation for in tegration point values, a new method inspired by Van Leer is constructed. T he new method is based on direct convection of integration point values wit hout intervention of nodal point values. The Molenkamp test and a so-called block test were executed to check the pe rformance and stability of the convection scheme. From these tests it is co ncluded that the new convection scheme shows accurate results. The scheme i s extended to an ALE-algorithm. An extrusion process was simulated to test the applicability of the scheme to engineering problems. It is concluded th at direct convection of integration point values with the presented algorit hm leads to accurate results and that it can be applied to ALE-simulations. Copyright (C) 2000 John Wiley & Sons, Ltd.