An intelligent nonlinear meta element for elastoplastic continua: deep learning using a new Time-distributed Residual U-Net architecture

Abstract

Substructuring is a model order reduction technique that accelerates the finite element method in solid mechanics. In this improved hybrid substructuring approach, methods from computational intelligence empower a reduced-order meta element. We propose a nonlinear and inelastic intelligent meta element for history-dependent boundary value problems. Fully compatible with conventional finite elements, it can be used to assemble larger structures. Within the intelligent meta element, a new deep neural network architecture composed of convolutions and recursions, the Time-distributed Residual U-Net (TRUNet), learns to solve the history-dependent spatial regression problem. The TRUNet automatically creates and updates the internal history variables necessary for the mechanical problem. Based on a new data generation strategy, data from a wide variety of use-cases train the neural network. An interface connects the neural network and the finite element method using a new data pre- and post-processing strategy. In three numerical demonstrations of elastoplastic continua, the intelligent meta element performs well, exhibiting low errors on a separate test dataset of several thousand samples. The intelligent reduced-order models compute considerably faster and achieve excellent approximations of the displacements, stresses, and forces.