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Classically, the constitutive behavior of materials is described eitherphenomenologically, or by homogenization approaches. Phenomenologicalapproaches are computationally very efficient, but are limited for complexnon-linear and irreversible mechanisms. Such complex mechanisms can bedescribed well by computational homogenization, but respective FE$^2$computations are very expensive. As an alternative way, neural networks havebeen proposed for constitutive modeling, using either experiments orcomputational homogenization results for training. However, the application ofthis method to irreversible material behavior is not trivial. The presentcontribution presents a hybrid methodology to embed neural networks into theestablished framework of rate-independent plasticity. Both, the yield functionand the evolution equations of internal state variables are represented byneural networks. Respective training data for a foam material are generatedfrom RVE-simulations under monotonic loading. It is demonstrated that thishybrid multi-scale neural network approach (HyMNNA) allows to simulateefficiently even the anisotropic elastic-plastic behavior of foam structureswith coupled anisotropic evolution of damage and non-associated plastic flow.

A hybrid approach to simulate the homogenized irreversible elastic-plastic deformations and damage of foams by neural networks