  (Artificial) neural networks have become increasingly popular in mechanics to
accelerate computations with model order reduction techniques and as universal
models for a wide variety of materials. However, the major disadvantage of
neural networks remains: their numerous parameters are challenging to interpret
and explain. Thus, neural networks are often labeled as black boxes, and their
results often elude human interpretation. In mechanics, the new and active
field of physics-informed neural networks attempts to mitigate this
disadvantage by designing deep neural networks on the basis of mechanical
knowledge. By using this a priori knowledge, deeper and more complex neural
networks became feasible, since the mechanical assumptions could be explained.
However, the internal reasoning and explanation of neural network parameters
remain mysterious.
  Complementary to the physics-informed approach, we propose a first step
towards a physics-informing approach, which explains neural networks trained on
mechanical data a posteriori. This novel explainable artificial intelligence
approach aims at elucidating the black box of neural networks and their
high-dimensional representations. Therein, the principal component analysis
decorrelates the distributed representations in cell states of RNNs and allows
the comparison to known and fundamental functions. The novel approach is
supported by a systematic hyperparameter search strategy that identifies the
best neural network architectures and training parameters. The findings of
three case studies on fundamental constitutive models (hyperelasticity,
elastoplasticity, and viscoelasticity) imply that the proposed strategy can
help identify numerical and analytical closed-form solutions to characterize
new materials.
