Dynamic and adaptive mesh-based graph neural network framework for simulating displacement and crack fields in phase field models

TL;DR

This paper introduces ADAPT-GNN, a dynamic mesh-based graph neural network framework that efficiently emulates phase field simulations of crack propagation, achieving high accuracy and significant computational speed-ups.

Contribution

The paper presents a novel adaptive mesh-based GNN framework that combines ML and AMR for fast, accurate phase field fracture simulations with dynamic mesh representation.

Findings

Achieves 15-36x speed-up over traditional phase field models.

High accuracy in predicting displacement and crack fields.

Effective emulation of complex fracture processes.

Abstract

Fracture is one of the main causes of failure in engineering structures. Phase field methods coupled with adaptive mesh refinement (AMR) techniques have been widely used to model crack propagation due to their ease of implementation and scalability. However, phase field methods can still be computationally demanding making them unfeasible for high-throughput design applications. Machine learning (ML) models such as Graph Neural Networks (GNNs) have shown their ability to emulate complex dynamic problems with speed-ups orders of magnitude faster compared to high-fidelity simulators. In this work, we present a dynamic mesh-based GNN framework for emulating phase field simulations of crack propagation with AMR for different crack configurations. The developed framework - ADAPTive mesh-based graph neural network (ADAPT-GNN) - exploits the benefits of both ML methods and AMR by describing the graph representation at each time-step as the refined mesh itself. Using ADAPT-GNN, we predict the evolution of displacement fields and scalar damage field (or phase field) with high accuracy compared to conventional phase field fracture model. We also compute crack stress fields with high accuracy using the predicted displacements and phase field parameter. Finally, we observe speed up of 15-36x compared to serial execution of the phase field model.