Approximating Fracture Paths in Random Heterogeneous Materials: A Probabilistic Learning Perspective
Publication: Journal of Engineering Mechanics
Volume 150, Issue 8
Abstract
Approximation frameworks for phase-field models of brittle fracture are presented and compared in this work. Such methods aim to address the computational cost associated with conducting full-scale simulations of brittle fracture in heterogeneous materials where material parameters, such as fracture toughness, can vary spatially. They proceed by combining a dimension reduction with learning between function spaces. Two classes of approximations are considered. In the first class, deep learning models are used to perform regression in ad hoc latent spaces. PCA-Net and Fourier neural operators are specifically presented for the sake of comparison. In the second class of techniques, statistical sampling is used to approximate the forward map in latent space, using conditioning. To ensure proper measure concentration, a reduced-order Hamiltonian Monte Carlo technique (namely, probabilistic learning on manifold) is employed. The accuracy of these methods is then investigated on a proxy application where the fracture toughness is modeled as a non-Gaussian random field. It is shown that the probabilistic framework achieves comparable performance in the sense while enabling the end-user to bypass the art of defining and training deep learning models.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Financial support of the National Science Foundation (NSF) under Grant DGE-2022040 is gratefully acknowledged. The authors thank Prof. John Dolbow for useful discussions regarding the phase-field method and its implementation.
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Journal of Engineering Mechanics
Volume 150 • Issue 8 • August 2024
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© 2024 American Society of Civil Engineers.
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Received: Oct 13, 2023
Accepted: Mar 15, 2024
Published online: Jun 6, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 6, 2024
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