On the mesh motion for ALE modeling of metal forming processes

Abstract

Arbitrary Lagrangian–Eulerian finite element method is being increasingly used for simulation of metal-forming operations, due to its capability to combine the features of both Lagrangian and Eulerian approaches in a single analysis. An important consideration in applying this approach is an algorithm which decides upon the motion of all degrees of freedom of the finite element mesh in every step of the analysis, such that the resulted mesh retains an optimal shape and condition. Such an algorithm has to be effective, general, and computationally efficient.

In this paper, an overview of the mesh motion problem is provided in which guidelines are given for designing mesh motion strategies for particular problems, and numerical schemes are proposed for moving the mesh on external boundaries and in the interior of the body consistent with the ALE principles. Some numerical examples are provided which demonstrate that with suitable mesh motion schemes, ALE formulation can be used effectively to solve problems which are otherwise difficult to solve in Lagrangian or Eulerian frameworks.