On the interplay between the solid deformation and fluid flow during the solidification of a metallic alloy

During solidification in casting processes, metallic alloys undergo a continuous transition from liquid to solid by passing a semi-solid or mushy state. In this contribution, we present a continuum-mechanical model describing the deformation and solidification using the thermodynamically consistent theory of porous media (TPM). The model is based on two constituents, namely an elasto-viscoplastic solid skeleton and a viscous pore fluid. The balance equations are formulated on the macroscale and the exchange of mass, species, momentum and energy between the constituents is expressed. Between both constituents a local thermal equilibrium is assumed. The initial boundary value problem is solved by a numerical solution scheme based on mixed Galerkin finite elements. The velocity of the solid skeleton, the pressure of the pore fluid, the common temperature and the chemical compositions are taken as the primary unknown field variables.