A mixed variational formulation for the solution of Norton-Hoff viscoplastic flows

The Norton-Hoff viscoplastic formulation is obtained from the viscoplastic potential convenient to derive the variational and the weak forms equivalent to the equilibrium equations. The general proposed formulation takes into account isotropic hardening and temperature effects. The proper linearisation of the weak form leads to the consistent operator expressed in analytical form. The penalty technique is examined to insure volume constraints due to the isochoric viscoplastic flow; with an associated three-field Variational form, the direct determination of the pressure field and consequently the stress field is possible. Numerical solutions compared with analytical ones are very relevant. At least, reference finite element models for two-roll hot piercing are developed with pertinent results concerning the tube state variables. (C) 1997 Elsevier Science Ltd.