Exploring energy minimization to model strain localization as a strong discontinuity using Physics Informed Neural Networks

TL;DR

This paper proposes a novel approach using Physics Informed Neural Networks to model strain localization as a sharp discontinuity in elastoplastic solids through energy minimization, demonstrating feasibility with 1D and 2D examples.

Contribution

It introduces a variational neural network framework for predicting displacement jumps and their locations in solids, integrating energy minimization with deep learning.

Findings

Feasibility demonstrated in 1D and 2D numerical examples.

Neural network architecture effectively captures localization phenomena.

Energy minimization approach successfully models strain localization as a discontinuity.

Abstract

We explore the possibilities of using energy minimization for the numerical modeling of strain localization in solids as a sharp discontinuity in the displacement field. For this purpose, we consider (regularized) strong discontinuity kinematics in elastoplastic solids. The corresponding mathematical model is discretized using Artificial Neural Networks (ANNs), aiming to predict both the magnitude and location of the displacement jump from energy minimization, $\textit{i.e.}$, within a variational setting. The architecture takes care of the kinematics, while the loss function takes care of the variational statement of the boundary value problem. The main idea behind this approach is to solve both the equilibrium problem and the location of the localization band by means of trainable parameters in the ANN. As a proof of concept, we show through both 1D and 2D numerical examples that the computational modeling of strain localization for elastoplastic solids using energy minimization is feasible.