DEDEM: Discontinuity Embedded Deep Energy Method for solving fracture mechanics problems

TL;DR

DEDEM introduces a novel neural network approach that effectively models fracture mechanics with discontinuities, achieving higher accuracy and efficiency than traditional methods by embedding discontinuous features directly into the neural network input.

Contribution

The paper proposes DEDEM, a new neural network method that embeds discontinuous features for improved modeling of fracture mechanics problems.

Findings

DEDEM accurately models crack behaviors in various fracture scenarios.

DEDEM outperforms existing domain decomposition methods in efficiency and accuracy.

The method effectively handles interfaces and internal boundaries with discontinuities.

Abstract

Physics-Informed Neural Networks (PINNs) have aroused great attention for its ability to address forward and inverse problems of partial differential equations. However, approximating discontinuous functions by neural networks poses a considerable challenge, which results in high computational demands and low accuracy to solve fracture mechanics problems within standard PINNs framework. In this paper, we present a novel method called Discontinuity Embedded Deep Energy Method (DEDEM) for modeling fracture mechanics problems. In this method, interfaces and internal boundaries with weak/strong discontinuities are represented by discontinuous functions constructed by signed distance functions, then the representations are embedded to the input of the neural network so that specific discontinuous features can be imposed to the neural network solution. Results demonstrate that DEDEM can accurately model the mechanical behaviors of cracks on a large variety of fracture problems. Besides, it is also found that DEDEM achieves significantly higher computational efficiency and accuracy than the existing methods based on domain decomposition techniques.