  We propose an extension of the cyclic hardening plasticity model formulated
by Armstrong and Frederick which includes micropolar effects. Our micropolar
extension establishes coercivity of the model which is otherwise not present.
We study then existence of solutions to the quasistatic, rate-independent
Armstrong-Frederick model with Cosserat effects which is, however, still of
non-monotone, non-associated type. In order to do this, we need to relax the
pointwise definition of the flow rule into a suitable weak energy-type
inequality. It is shown that the limit in the Yosida approximation process
satisfies this new solution concept. The limit functions have a better
regularity than previously known in the literature, where the original
Armstrong-Frederick model has been studied.
