Thermodynamically consistent Recurrent Neural Networks to predict non linear behaviors of dissipative materials subjected to non-proportional loading paths

The present work aims at proposing a hybrid physics-AI based model to predict non-linear mechanical behaviors of dissipative materials. By introducing a specific Neural Network architecture called Thermodynamically Consistent Recurrent Neural Networks (ThC-RNN), this study proposes a new paradigm for the simulation of dissipative materials under complex loading conditions. The design of such architecture allows to take into account the material loading history subjected to multi-axial and non-proportional loading paths, similarly to internal variables for homogeneous materials. A special focus has been given to the respect of thermodynamics principles in the ThC-RNN model by introducing specific thermodynamical constraints during the training phase. Finally, the model’s reliability has been tested on different plasticity models once the training is completed. It is shown that thermodynamic consistency improves significantly the prediction capabilities of the ThC-RNN model, considering several outputs such as stress tensor and tangent modulus components, state variables and mechanical work rate partition (recoverable part, irrecoverable part and dissipative part)