Phase-Field Modeling of Fracture with Physics-Informed Deep Learning

TL;DR

This paper introduces a physics-informed deep learning approach using the deep Ritz method to model complex fracture processes within phase-field modeling, demonstrating its effectiveness on benchmark problems.

Contribution

It presents a novel neural network-based variational method for simulating fracture phenomena, addressing challenges in energy landscape approximation and optimization within phase-field models.

Findings

Method accurately captures crack nucleation, propagation, and branching.

Results agree qualitatively and quantitatively with finite element solutions.

Approach is robust across different neural network initializations.

Abstract

We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of brittle fracture. We elucidate the challenges related to the neural-network-based approximation of the energy landscape, and the ability of an optimization approach to reach the correct energy minimum, and we discuss the choices in the construction and training of the neural network which prove to be critical to accurately and efficiently capture all the relevant fracture phenomena. The developed method is applied to several benchmark problems and the results are shown to be in qualitative and quantitative agreement with the finite element solution. The robustness of the approach is tested by using neural networks with different initializations.