Application of the arbitrary Eulerian Lagrangian finite element formulation to the thermomechanical simulation of casting processes, with focus on pipe shrinkage prediction
Résumé
The Arbitrary Lagrangian-Eulerian formulation (ALE) has become an indispensable component of finite element thermomechanical computations of casting processes. As it is an intermediate formulation between the Lagrangian formulation (material convected mesh) and the Eulerian one (fixed mesh), it allows the simultaneous computation of important phenomena: Deformation and stresses affecting solidified regions, yielding the computation of air gap evolution at part/mold interfaces. In such regions, the formulation is essentially Lagrangian. Thermosolutal convection flow in the non solidified regions; here the ALE formulation tends to a pure Eulerian one (stationary mesh). Free surface evolution at top of risers, leading to the prediction of pipe defects (macroshrinkage). In this case the ALE formulation allows the follow up of the free surface. After a brief reminder of the constitutive equations to be used in thermomechanical modeling of solidification, the mechanical equations are presented and their resolution in the context of FEM-ALE. We insist on the transport analysis, a key-point of ALE, and present a validation of the original scheme that is used here. Finally, we focus on the prediction of pipe shrinkage formation and show two industrial examples.
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