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This article deals with a viscoplastic material model of overstress type. Themodel is based on a multiplicative decomposition of the deformation gradientinto elastic and inelastic part. An additional multiplicative decomposition ofinelastic part is used to describe a nonlinear kinematic hardening ofArmstrong-Frederick type.  Two implicit time-stepping methods are adopted for numerical integration ofevolution equations, such that the plastic incompressibility constraint isexactly satisfied. The first method is based on the tensor exponential. Thesecond method is a modified Euler-Backward method. Special numerical tests showthat both approaches yield similar results even for finite inelasticincrements.  The basic features of the material response, predicted by the material model,are illustrated with a series of numerical simulations.

Finite strain viscoplasticity with nonlinear kinematic hardening: phenomenological modeling and time integration