  Classically, the constitutive behavior of materials is described either
phenomenologically, or by homogenization approaches. Phenomenological
approaches are computationally very efficient, but are limited for complex
non-linear and irreversible mechanisms. Such complex mechanisms can be
described well by computational homogenization, but respective FE$^2$
computations are very expensive. As an alternative way, neural networks have
been proposed for constitutive modeling, using either experiments or
computational homogenization results for training. However, the application of
this method to irreversible material behavior is not trivial. The present
contribution presents a hybrid methodology to embed neural networks into the
established framework of rate-independent plasticity. Both, the yield function
and the evolution equations of internal state variables are represented by
neural networks. Respective training data for a foam material are generated
from RVE-simulations under monotonic loading. It is demonstrated that this
hybrid multi-scale neural network approach (HyMNNA) allows to simulate
efficiently even the anisotropic elastic-plastic behavior of foam structures
with coupled anisotropic evolution of damage and non-associated plastic flow.
