Hybrid data-driven and physics-informed regularized learning of cyclic
  plasticity with Neural Networks
Stefan Hildebrand Sandra Klinge
An extendable, efficient and explainable Machine Learning approach is
proposed to represent cyclic plasticity and replace conventional material
models based on the Radial Return Mapping algorithm. High accuracy and
stability by means of a limited amount of training data is achieved by
implementing physics-informed regularizations and the back stress information.
The off-loading of the Neural Network is applied to the maximal extent. The
proposed model architecture is simpler and more efficient compared to existing
solutions from the literature, while representing a complete three-dimensional
material model. The validation of the approach is carried out by means of
surrogate data obtained with the Armstrong-Frederick kinematic hardening model.
The Mean Squared Error is assumed as the loss function which stipulates several
restrictions: deviatoric character of internal variables, compliance with the
flow rule, the differentiation of elastic and plastic steps and the
associativity of the flow rule. The latter, however, has a minor impact on the
accuracy, which implies the generalizability of the model for a broad spectrum
of evolution laws for internal variables. Numerical tests simulating several
load cases are shown in detail and validated for accuracy and stability.