This thesis addresses a continuum-mechanical , two-phase, two-scale model for thermally driven solidification processes. The macro-scale covers the thermal-mechanical loading during processing like the cooling process, the thermal shrinkage and its stress response as well as the shaping, respectively. Therefore, the theory of porous media (TPM) is utilized to describe materials at multiple aggregate states. Furthermore, strong thermal coupling as well as finite plasticity superimposed by a secondary creep power law are utilized to capture the material behaviour at all temperatures. Moreover, the micro-scale predicts the phase transition during solidification. Therefore, the phase-field theory including its double-well potential has been used in order to describe the solid and liquid material physical states as well as the smeared mushy zone, which contains both phases simultaneously, respectively. From the numerical point of view, the finite element method and the finite difference method have been utilized to solve the macro- and the micro-scale. Finally, an micro-macro inter-scale linking scheme as well as an two examples, a solidification experiment and a Bridgmen ofen simulation are presented.
