  Herein, we present a new data-driven multiscale framework called
FE${}^\text{ANN}$ which is based on two main keystones: the usage of
physics-constrained artificial neural networks (ANNs) as macroscopic surrogate
models and an autonomous data mining process. Our approach allows the efficient
simulation of materials with complex underlying microstructures which reveal an
overall anisotropic and nonlinear behavior on the macroscale. Thereby, we
restrict ourselves to finite strain hyperelasticity problems for now. By using
a set of problem specific invariants as the input of the ANN and the Helmholtz
free energy density as the output, several physical principles, e.g.,
objectivity, material symmetry, compatibility with the balance of angular
momentum and thermodynamic consistency are fulfilled a priori. The necessary
data for the training of the ANN-based surrogate model, i.e., macroscopic
deformations and corresponding stresses, are collected via computational
homogenization of representative volume elements (RVEs). Thereby, the core
feature of the approach is given by a completely autonomous mining of the
required data set within an overall loop. In each iteration of the loop, new
data are generated by gathering the macroscopic deformation states from the
macroscopic finite element (FE) simulation and a subsequently sorting by using
the anisotropy class of the considered material. Finally, all unknown
deformations are prescribed in the RVE simulation to get the corresponding
stresses and thus to extend the data set. The proposed framework consequently
allows to reduce the number of time-consuming microscale simulations to a
minimum. It is exemplarily applied to several descriptive examples, where a
fiber reinforced composite with a highly nonlinear Ogden-type behavior of the
individual components is considered.
