A fixed-mesh Eulerian-Lagrangian approach for stress analysis in continuous casting

We present a method for the analysis of the strains and stresses developed in the solidified portion of a metal strand during the continuous casting process. Steady-state conditions are assumed. The solidified metal is modelled as a standard inelastic solid with isotropic hardening and von Mises yield criterion. Constitutive equations are formulated over the material particles (Lagrangian approach) that instantaneously occupy a fixed domain attached to the casting machine, which is discretized (Eulerian approach). Particle tracking, needed to record the deformation history at each fixed sampling point, becomes trivial because of the usual hypothesis of constant and homogeneous advection velocity. Backward-Euler (implicit) finite differences and mixed finite elements are used for time and spatial discretization, respectively. The resulting non-linear algebraic equations are solved using the Newton–Raphson method. Copyright q 2006 John Wiley & Sons, Ltd