Modelling of the thermomechanical coupling during hot forming of viscoplastic materials

In the present paper, a strategy for solving transient thermoviscoplastic problems is described. The general thermal and mechanical coupling phenomena are discussed by assuming material properties to be temperature-dependent and accounting for the mechanical terms in the non-stationary heat conduction equation. Time integration is carried out with an implicit scheme. An interesting version of the three-field approach is presented to obtain an accurate solution for the stress field. Finally, a global product coupling algorithm, in which the unknown nodal velocities and temperatures are solved with a two-step solution procedure is suggested. The proposed fractional step method partitions the initial coupled problem into an isothermal viscoplastic problem followed by a purely heat conduction problem at fixed configuration. Applications in metal forming analyses involving full thermomechanical coupling conclude the paper.