In this paper we describe a method for the construction of radial return algorithms to the plasticity models discussed in Alber . For the classical examples this shows that the algorithms in Simo-Hughes  can be derived by this method in a systematic way. We apply the method to viscoplasticity with nonlinear isotropic and kinematic hardening. The combination of parallel multigrid methods with the radial return algorithm results in a very efficient algorithm. The performance of the method is illustrated by a numerical example.
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