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