Physics-based Machine Learning for Computational Fracture Mechanics

Abstract: This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft constraints in loss functions and enforcing boundary conditions via collocation points, our framework integrates physical principles, such as the governing equations and constraints, directly into the neural network architecture. This approach eliminates the dependency on problem-specific retraining for new boundary value problems, ensuring adaptability and consistency. By embedding constitutive behavior into the network's foundational design, our method represents a significant step toward unifying material modeling with machine learning for computational fracture mechanics. Specifically, a feedforward neural network is designed to embed physical laws within its architecture, ensuring thermodynamic consistency. Building on this foundation, synthetic datasets generated from finite element-based phase-field simulations are employed to train the proposed framework, focusing on capturing the homogeneous responses of brittle and ductile fractures. Detailed analyses are performed on the stored elastic energy and the dissipated work due to plasticity and fracture, demonstrating the capability of the framework to predict essential fracture features. The proposed physics-based machine learning framework overcomes the shortcomings of classical machine learning models, which rely heavily on large datasets and lack guarantees of physical principles. By leveraging its physics-integrated design, the physics-based machine learning framework demonstrates exceptional performance in predicting key properties of brittle and ductile fractures with limited training data.