Anisotropic finite plasticity with combined hardening and application to sheet metal forming

In this work, we discuss a finite strain constitutivemodel combining both nonlinear isotropic and nonlinear kinematic hardening. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The evolution of elastic anisotropy is represented by defining the Helmholtz free energy as a function of a family of evolving structural tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the plastic deformation and on the structural tensors. The integration of the evolution equations has been performed by means of a new form of the exponential map algorithm which automatically satisfies plastic incompressibility and retains the symmetry of the internal variables. The model has been validated based on experimental data and simulations of draw bending of a sheet strip and deep drawing of a cup.