Physics-Informed Neural Network modeling of Cyclic Plasticity for steel alloy 4130

An efficient and explainable Machine Learning approach is presented replacing conventional material models based on the Radial Return Mapping algorithm for the constitutive modeling of cyclic plasticity. The presented model architecture is simpler and more efficient compared to existing solutions and needs approximately only half of NN parameters, while representing a complete three-dimensional material model. High accuracy and stability are achieved by physics-informed regularizations and including back stress information. The approach is validated by means of a case study for steel alloy 4130. The loss function is designed to stipulate several qualitative restrictions: deviatoric character of internal variables, compliance with the flow rule, the differentiation between elastic and plastic steps. The associativity of the flow rule, has only a minor impact on the accuracy, which implies the generalizability of the approach for a broad spectrum of materials undergoing plastic deformation. The validation shows cyclic stability and deviations in normal directions of less than 2% at peak values which is comparable to the order of measurement inaccuracies.