A continuum theory for the thermomechanics of solidification

Abstract A general theory for the phenomenon of solidification is presented in which the coupling between the thermal and kinematical fields is fully taken into account. The resulting model descsribes the liquid region as an ordinary Newtonian liquid and the solid phase as an elastic material. In the case of multi-component solidification it allows for the existence of a mixed region separating the pure phases whose behavior is modeled as a non-linear viscoelastic material. After a preliminary analysis of the jump conditions across the singular surface separating the two phases, the strong interdependence between the thermomechanical field, the geometry of the singular surface and the freezing temperature θf is examined in detail. A simple one-dimensional problem (Boussinesq problem) has been discussed to show how only a dynamical theory can predict with reasonable accuracy the final shape of the solid.