  The mathematical formulation of constitutive models to describe the
path-dependent, i.e., inelastic, behavior of materials is a challenging task
and has been a focus in mechanics research for several decades. There have been
increased efforts to facilitate or automate this task through data-driven
techniques, impelled in particular by the recent revival of neural networks
(NNs) in computational mechanics. However, it seems questionable to simply not
consider fundamental findings of constitutive modeling originating from the
last decades research within NN-based approaches. Herein, we propose a
comparative study on different feedforward and recurrent neural network
architectures to model inelasticity. Within this study, we divide the models
into three basic classes: black box NNs, NNs enforcing physics in a weak form,
and NNs enforcing physics in a strong form. Thereby, the first class of
networks can learn constitutive relations from data while the underlying
physics are completely ignored, whereas the latter two are constructed such
that they can account for fundamental physics, where special attention is paid
to the second law of thermodynamics in this work. Conventional linear and
nonlinear viscoelastic as well as elastoplastic models are used for training
data generation and, later on, as reference. After training with random walk
time sequences containing information on stress, strain, and, for some models,
internal variables, the NN-based models are compared to the reference solution,
whereby interpolation and extrapolation are considered. Besides the quality of
the stress prediction, the related free energy and dissipation rate are
analyzed to evaluate the models. Overall, the presented study enables a clear
recording of the advantages and disadvantages of different NN architectures to
model inelasticity and gives guidance on how to train and apply these models.
