Recurrent neural networks as a physics-based self-learning solver to satisfy plane stress viscoplasticity undergoing isotropic damage

The present study introduces a new self-learning framework based on a recurrent neural network to compute the nonlinear viscoplastic response of plate structures undergoing isotropic damage. The neural network comprising Legendre Memory Unit (LMU) cells and dense transformations is pretrained with a combination of data-driven and physics-based loss functions. Once pretrained, the model is deployed in the explicit integration scheme to predict the strain increment in the thickness direction satisfying plane stress condition. This results in elimination/reduction in the iterations required to fulfill the plane stress condition and leads to faster convergence since the neural network replaces the root-finding methods. The proposed self-learning method differentiates itself from the well-known Physics-Informed Neural Networks (PINNs) since the neural network model self-learns online through the proposed physics-based loss term without the need for data. We compare the results of the Neural Network-enhanced integration scheme to validate the proposed method with those of the classical explicit integration scheme.