Formulation of an implicit algorithm for finite deformation viscoplasticity

Within the framework of additive plasticity, an objective stress update algorithm has been proposed. The procedure is implemented in such way that the extension from a standard small strain FE code to the ®nite strain range is straightforward, and objectivity can be retained for any choice of the intermediate con®guration. The additional computational cost only includes some geometrical manipulations. For the Newton±Raphson iteration method, a closed-form solution of the consistent tangent is derived by direct linearization of the stress update algorithm. Numerical examples show a quadratic rate of convergence with the proposed viscoplastic model. The analysis of a tensile test ®rst shows a shear band with a ®nite thickness independent of the ®nite element size. At large deformation, the shear band pattern transforms into a necking failure mode. As a second example, a thin sheet tensile test is analyzed. A necking failure mode leads to global softening even though, locally, the material is still hardening. Although viscoplastic regularization is used, the results still show a mesh dependence for deformations over 40%.