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

Mechanics Research Communications, vol. 142, pp. 104347

Abstract

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. • The LMU-based model acts as a nonlinear self-learning solver to satisfy the plane stress condition σ 33 = 0 . • The iterations required to achieve the plane stress condition are reduced/eliminated. • The NN model receives constant feedback from the physics-based loss function ensuring convergence. • The internal variables of the LMU model trace the evolution of σ 33 = 0 in the nonlinear domain for each Gaussian point.

Authors 3

1. Saurabh Balkrishna Tandale Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52056 Aachen, Germany

2. Vasileios Polydoras Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52056 Aachen, Germany

3. Marcus Stoffel corresponding Aachen Institute of General Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of General Mechanics, RWTH Aachen University, Eilfschornsteinstraße 18, 52056 Aachen, Germany