Finite element implementation of an orthotropic plasticity model for sheet metal forming simulations

In this work, the implementation procedures for the user Fortran subroutines of the commercial finite element code ABAQUS are described for the particular case of linear elasticity and a plasticity model proposed within the context of the plastic flow theory along with the isotropic work-hardening assumption. The general 3D case is firstly presented and detailed for the implicit and explicit integration techniques available in the ABAQUS code. Afterwards, the equations for the particular plane-stress state are outlined. The corresponding procedures are applied to a plane-stress orthotropic plasticity model. Finally, the implemented user subroutines are validated by means of numerical simulations of sheet metal forming experiments, namely, the hemispherical punch stretching and cup-drawing. The comparisons of the predicted either radial strains or earing formation with the measured data obtained for an IF steel and a tinplate food-can shows the pertinent conditioning of the user subroutines as well as the importance of an accurate description of the range of stresses states involved in sheet metal forming processes.