An ALE‐FEM approach to the thermomechanics of solidification processes with application to the prediction of pipe shrinkage

Michel Bellet, Olivier Jaouen, Isabelle Poitrault
2005 International journal of numerical methods for heat & fluid flow  
The present paper addresses the computer modelling of pipe formation in castings. As a preliminary, a brief review of the current state-of-the-art in pipe shrinkage computation is presented: most of existing methods are based on thermal considerations only. In the current paper, it is demonstrated that this typical evolution of the free surface, originated by shrinkage at solidification front and compensating feeding liquid flow, can be effectively approached by a thermomechanical analysis in
more » ... e frame of the finite element method (FEM) and the arbitrary Lagrangian-Eulerian (ALE) formulation. In a first part, the constitutive equations that have to be considered in thermomechanical computations are presented. This point is central because the cast alloy is simultaneously present in liquid, mushy and solid state. Then the main lines of the mechanical finite element resolution are given, insisting on the fact that it permits the concurrent computation of stresses and strains in solidified areas and of liquid flow in still liquid or mushy zones. A detailed presentation of the Eulerian-Lagrangian formulation follows, explaining the connection between the Lagrangian and the quasi Eulerian zones, and the treatment of free surfaces. Finally, an example of application to an industrial casting is given.
doi:10.1108/09615530510578410 fatcat:7gidmgibazeqdbon7f4spocyry