  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.
