Constitutive models of steel under continuous casting conditions

We review in this paper a series of constitutive equations that describe the behavior of steels at elevated temperatures, laying emphasis upon continuous casting processes. The different laws are situated in an appropriate thermodynamic context, enabling the straightforward multiaxial generalization of uniaxial relationships proposed on a pure experimental basis. Plastic and viscoplastic standard materials are mainly considered, including models that split the instantaneous and creep components of the irreversible deformation. Unified models without a yield criterion are also treated. Predictions of different models for steels with the same carbon content are shown throughout the work.