Physics-Based Self-Learning Recurrent Neural Network enhanced time integration scheme for computing viscoplastic structural finite element response

Abstract

In the current study, we present an application to the class of deep learning known as the Physics Informed Neural Networks (PINNs), more specifically we develop a new implicit material integration scheme based on Recurrent Neural Network (RNN). In this study, we refer to it as the Recurrent Enhanced Implicit Integration Scheme (REIIS). We illustrate how to incorporate the constitutive relations into REIIS and explore its application to Lemaitre–Chaboche viscoplastic model. Whilst common applications in this class of deep learning utilize feed-forward neural networks (FFNN) for training, we propose a combination of the Long Term Short Memory (LSTM) network with FFNNs for an accurate representation of the state variables. Furthermore, with the present strategy, we combine the data-driven approach of replacing the material behavior with NN along with its ability to learn continuously through physical laws. To validate the approach, we test the results of the framework with the numerical solution obtained with Finite Element Method (FEM) for Reissner–Mindlin plate elements at different strain rates. We further observe that obeying physical constraints leads to improved robustness in the learning of REIIS and broadens the scope of integrating the NNs in FEM.