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Title: FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

Abstract

This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.

Authors:
 [1]; ORCiD logo [1]
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  1. Columbia Univ., New York, NY (United States)
Publication Date:
Research Org.:
Columbia Univ., New York, NY (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE), Nuclear Energy University Program (NEUP); USDOE
OSTI Identifier:
1801240
Alternate Identifier(s):
OSTI ID: 1592511
Grant/Contract Number:  
NE0008534
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 362; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; fast Fourier transform; multi-phase-field fracture; higher-order phase field fracture; anisotropic cracks; polycrystal; salt

Citation Formats

Ma, Ran, and Sun, WaiChing. FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials. United States: N. p., 2020. Web. doi:10.1016/j.cma.2019.112781.
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Ma, Ran, & Sun, WaiChing. FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials. United States. https://doi.org/10.1016/j.cma.2019.112781
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Ma, Ran, and Sun, WaiChing. Mon . "FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials". United States. https://doi.org/10.1016/j.cma.2019.112781. https://www.osti.gov/servlets/purl/1801240.
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@article{osti_1801240,
title = {FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials},
author = {Ma, Ran and Sun, WaiChing},
abstractNote = {This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.},
doi = {10.1016/j.cma.2019.112781},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = 362,
place = {United States},
year = {Mon Jan 20 00:00:00 EST 2020},
month = {Mon Jan 20 00:00:00 EST 2020}
}
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https://doi.org/10.1016/j.cma.2019.112781
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