Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with neural networks

Abstract 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 (NN) is applied to the maximal extent. The proposed model architecture is simpler and more efficient compared to existing solutions from the literature using approximately only half the amount of NN parameters, while representing a complete three-dimensional material model. The validation of the approach is carried out by means of results 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 presented in detail. 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.