Physics-based Machine Learning for Computational Fracture Mechanics

TL;DR

The paper tackles the computational bottleneck of multiscale fracture modeling by embedding governing equations and constitutive laws directly into a CNN-based architecture, enabling thermodynamically consistent predictions that generalize across boundary-value problems without problem-specific retraining. It trains the network on synthetic FE-based phase-field data to capture brittle and ductile fracture responses with limited data, and demonstrates substantial speedups over conventional FEM while preserving high accuracy in predicting homogenized stresses. A transfer-learning strategy shows rapid and accurate adaptation to new microstructures, highlighting practical benefits for design workflows. The work significantly accelerates micro-to-macro simulations in heterogeneous materials and lays groundwork for extending to inelastic behavior and real experimental datasets.

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.

Figures (13)

• Figure 1: Computational micro-to-macro transition approach of heterogeneous materials.
• Figure 2: Periodic microstructure, where the surface of the $\cal{RVE}$ in (a) decomposes into two parts $\partial{\mathcal{B}}=\partial{\mathcal{B}}^+\cup\partial{\mathcal{B}}^-$ with normals ${\boldsymbol{\mathnormal n}}^+$ and ${\boldsymbol{\mathnormal n}}^-=-{\boldsymbol{\mathnormal n}}^+$ at associated points ${\boldsymbol{\mathnormal x}}^+\in\partial{\mathcal{B}}^+$ and ${\boldsymbol{\mathnormal x}}^-\in\partial{\mathcal{B}}^-$. (b) Periodic boundary conditions for the displacement.
• Figure 3: An example of a convolution operation.
• Figure 4: Example of Average Pooling operation
• Figure 5: Example of Max Pooling operation