Physics-based machine learning for computational fracture mechanics

Abstract This study introduces a physics-based machine learning ( $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> ML) framework for modeling both brittle and ductile fractures in elastic-viscoplastic materials. It integrates physical principles, including governing equations and constraints, directly into the neural network architecture. 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 fracture simulations are employed to train the proposed framework, focusing on capturing the homogeneous, one-dimensional fracture responses. 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 $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> ML 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 $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> ML framework demonstrates exceptional performance in predicting key properties of brittle and ductile fractures with limited training data. This ensures reliability, efficiency, and physical consistency, establishing a foundational approach for integrating machine learning with computational fracture mechanics.