Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks
This work addresses the need for efficient and explainable material models in computational mechanics, representing an incremental improvement by simplifying and enhancing existing neural network solutions for cyclic plasticity.
The authors tackled the problem of modeling cyclic plasticity by proposing a hybrid data-driven and physics-informed neural network approach to replace conventional material models, achieving high accuracy and stability with limited training data through physics-informed regularizations and back stress information.
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.