Anisotropic yield functions in a co-rotating reference frame

In metal forming simulations large deformations are often treated based on objective formulations. Large rotations are accounted for by rotating the stress tensor or approximating the rotation by some integration rule for the rate of rotation. For isotropic material behavior, this is easily done. For anisotropic material behavior however, not only the stresses, but also the relation between stress rate and strain rate must be updated. In this case it is easier to take a co-rotating reference frame and apply the constitutive relations on a strain measure that is neutralized for rigid body translations and rotations. This paper presents an algorithm that is based on the latter idea. The algorithm directly uses the increments in the deformation gradient, avoiding as much as possible to take time derivatives that should then be integrated subsequently. The algorithm is applied to a constitutive model including an initial anisotropic yield function and isotropic and kinematic hardening. The kinematic hardening makes use of a maximal back stress surface [1] to account for behavior observed in cyclic loading.