A peridynamic-informed deep learning model for brittle damage prediction

TL;DR

This paper introduces a novel deep learning model that integrates peridynamic theory with physics-informed neural networks to accurately predict damage and crack growth in brittle materials, improving convergence and capturing complex displacement patterns.

Contribution

The study presents a new PD-informed neural network that enforces peridynamic equations within the loss function, enhancing damage prediction accuracy and robustness in brittle material simulations.

Findings

Accurately predicts damage and crack propagation in brittle materials.

Outperforms high-fidelity methods in benchmark tests.

Demonstrates improved convergence and learning of complex displacement patterns.

Abstract

In this study, a novel approach that combines the principles of peridynamic (PD) theory with PINN is presented to predict quasi-static damage and crack propagation in brittle materials. To achieve high prediction accuracy and convergence rate, the linearized PD governing equation is enforced in the PINN's residual-based loss function. The proposed PD-INN is able to learn and capture intricate displacement patterns associated with different geometrical parameters, such as pre-crack position and length. Several enhancements like cyclical annealing schedule and deformation gradient aware optimization technique are proposed to ensure the model would not get stuck in its trivial solution. The model's performance assessment is conducted by monitoring the behavior of loss function throughout the training process. The PD-INN predictions are also validated through several benchmark cases with the results obtained from high-fidelity techniques such as PD direct numerical method and Extended-Finite Element Method. Our results show the ability of the nonlocal PD-INN to predict damage and crack propagation accurately and efficiently.