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A FEniCS implementation of the phase field method for quasi-static brittle fracture
Published in Higher Education Press
2019
Volume: 13
   
Issue: 2
Pages: 380 - 396
Abstract
In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature. © 2018, Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature.
About the journal
JournalFrontiers of Structural and Civil Engineering
PublisherHigher Education Press
ISSN20952430
Open AccessNo
Concepts (16)
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    Brittle fracture
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    Crack propagation
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    Cracks
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    Nonlinear equations
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    Open source software
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    Open systems
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    Partial differential equations
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    Bench-mark problems
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    COUPLED NONLINEAR SYSTEMS
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    DIFFUSION-TYPE EQUATIONS
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    DISCONTINUOUS SURFACES
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    FENICS
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    Finite element software
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    PHASE FIELD METHODS
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    VARIATIONAL THEORY
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    Phase transitions