The prediction of the structural response requires the constitutive description of the material from which the structure is built. For complex elastic-plastic anisotropic materials, analytical closed form constitutive models with sufficient accuracy may not exist. Concurrent modeling (i.e. FE^2) is extremely costly, in particular for larger three-dimensional structures. Alternatively, data driven approaches based on machine learning gains increasing attention. In this contribution such an approach will be presented for a periodic lattice material with cubic material symmetry and elastic-plastic parent material. Not only the elastic anisotropy is very pronounced, but also the initial yield surface and the hardening response is highly direction dependent. A periodic unit cell model is set up in the framework of the Finite Element Method to predict the non-linear stress response to strain controlled monotonic proportional loading. The resulting data base is used for training, testing, and validation of an artificial neural network. Additionally, energy considerations are included in terms of elastic recoverable and plastic dissipative contributions to distinguish between loading and unloading. Moreover, the predictive capabilities for (mildly) non-proportional strain histories is assessed. The AI-based constitutive model is implemented as VUMAT into ABAQUS/Explicit to run structural analyses. As example a cantilever beam formed by ten times hundred unit cells is studied under various loading conditions and the performance of the developed constitutive model is evaluated. Since the example beam is small enough to fully discretize the all lattice members, detailed comparison to the reference model is possible.