A residual control staggered solution scheme for the phase-field modeling of brittle fracture

•The phase-field staggered algorithm with a residual norm based stopping criterion.•An arbitrary porous steel microstructure exhibiting complex crack paths is analyzed.•The stopping criterion is highly important for achieving accuracy and efficiency.•Verification by numerical and experimental result...

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Bibliographic Details
Published in:Engineering fracture mechanics 2019-01, Vol.205, p.370-386
Main Authors: Seleš, Karlo, Lesičar, Tomislav, Tonković, Zdenko, Sorić, Jurica
Format: Article
Language:English
Subjects:
Abaqus
Algorithms
Brittle fracture
Computer simulation
Computing time
Criteria
Finite element method
Iterative methods
Mathematical models
Phase-field modeling
Staggered algorithm
Stopping criterion
Subroutines
Tracking problem
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Summary:•The phase-field staggered algorithm with a residual norm based stopping criterion.•An arbitrary porous steel microstructure exhibiting complex crack paths is analyzed.•The stopping criterion is highly important for achieving accuracy and efficiency.•Verification by numerical and experimental results available in literature.•Numerical implementation takes advantage of Abaqus FE software features. The phase-field approach to fracture modeling circumvents the crack-surface tracking problem by introducing the phase-field variable which separates the broken and unbroken material states through a smooth transition. However, very fine spatial discretization is required to resolve the smooth distribution of the phase-field regulated by a small length scale parameter. Thus, it can be computationally rather expensive when paired with an inefficient solution scheme. This contribution presents a comprehensive discussion on the use of a stopping criterion within the broadly used staggered algorithm. The stopping criterion of the iterative scheme based on the control of the residual norm is introduced and implemented in the finite element software Abaqus. It alleviates the problem of the common single iteration staggered algorithm, which requires fine loading incrementation to produce an accurate solution. The model verification is conducted on several standard benchmark tests and a porous microstructure exhibiting complex crack phenomena. The detailed discussions regarding the proposed implementation’s accuracy and CPU time usage are provided, demonstrating an improvement in computational efficiency with accurate results no longer dependent on the careful selection of loading incrementation. The algorithm codes in the form of the Abaqus user subroutines UMAT and UEL are publicly available on Mendeley data repository linked to this work.
ISSN:0013-7944
1873-7315
DOI:10.1016/j.engfracmech.2018.09.027