Application of a physically based constitutive model to metal forming analysis

A 3D constitutive equation for large elastoplastic deformation is derived by taking into account the energy stored in the residual microstress fields in plastically deformed material and its effect on subsequent plastic deformation: this model may be used to describe the non-linear behaviour of material at the onset of loading and unloading. Non-linear mixed isotropic and kinematic hardening, and the effects of temperature and strain rate on material properties, are also considered. Expressions with and without a yield surface are provided. A numerical algorithm which corresponds to the constitutive equation without a yield surface is proposed and the material-user-subroutine UMAT is programmed and embedded in the commercial software ABAQUS. The analyses of necking, upsetting and extrusion were used to validate the proposed constitutive model and the corresponding numerical approach in metal forming analysis.