The thermal analysis using standard linear tetrahedral finite elements may be severely affected by spurious local extrema in the regions affected by thermal shocks; conceivably discouraging the use of such elements as a result. The present work proposes three numerical models based on the mixed temperature/heat flux formulation to solve the unsteady thermal problem. Our new model, called the Mixed continuous formulation, should allow to improve the thermomechanical coupling effects during the simulation of 3D forming processes: the spatial model is based on the Galerkin approach with the linear tetrahedral P1/P1 mixed finite elements; time integration is based on an implicit scheme allowing better flexibility in the choice of time steps. For this study, the 3D finite element FORGE3® software, able to simulate strongly coupled thermomechanical problems and steel quenching, is required.
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