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Journal of Shanghai Jiaotong University (Science)

, Volume 23, Issue 1, pp 166–174 | Cite as

Implementation Details for the Phase Field Approaches to Fracture

  • Yongxing Shen (沈泳星)
  • Mostafa Mollaali
  • Yihuan Li (李毅环)
  • Weixin Ma (马维馨)
  • Jiahao Jiang (蒋家皓)
Article

Abstract

Phase field description of fracture is a very promising approach for simulating crack initiation, propagation, merging and branching. This method greatly reduces the implementation complexity, compared with discrete descriptions of cracks. In this work, we provide an overview of phase field models for quasistatic and dynamic cases. Afterward, we present useful vectors and matrices for the implementation of this method in two and three dimensions.

Key words

phase field approach to fracture variational fracture brittle fracture dynamic fracture variational integrator 

CLC number

O241.82 

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References

  1. [1]
    LANDAU L D, LIFSHITZ E M. Statistical physics [M]. Oxford: Pergamon Press, 1980.MATHGoogle Scholar
  2. [2]
    ARANSON I, KALATSKY V, VINOKUR V. Continuum field description of crack propagation [J]. Physical Review Letters, 2000, 85(1): 118.CrossRefGoogle Scholar
  3. [3]
    KARMA A, KESSLER D A, LEVINE H. Phase-field model of mode iii dynamic fracture [J]. Physical Review Letters, 2001, 87(4): 045501.CrossRefGoogle Scholar
  4. [4]
    HENRY H, LEVINE H. Dynamic instabilities of fracture under biaxial strain using a phase field model [J]. Physical Review Letters, 2004, 93(10): 105504.CrossRefGoogle Scholar
  5. [5]
    AMBATI M, GERASIMOV T, DE LORENZIS L. A review on phase-field models of brittle fracture and a new fast hybrid formulation [J]. Computational Mechanics, 2015, 55(2): 383–405.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    FRANCFORT G A, MARIGO J J. Revisiting brittle fracture as an energy minimization problem [J]. Journal of the Mechanics and Physics of Solids, 1998, 46(8): 1319–1342.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    BOURDIN B, FRANCFORT G A, MARIGO J J. Numerical experiments in revisited brittle fracture [J]. Journal of the Mechanics and Physics of Solids, 2000, 48(4): 797–826.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    BOURDIN B. Numerical implementation of the variational formulation for quasi-static brittle fracture [J]. Interfaces and Free Boundaries, 2007, 9(3): 411–430.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    BOURDIN B, MARIGO J J, MAURINI C, et al. Morphogenesis and propagation of complex cracks induced by thermal shocks [J]. Physical Review Letters, 2014, 112: 014301.CrossRefGoogle Scholar
  10. [10]
    TANNÉ E, LI T, BOURDIN B, et al. Crack nucleation in variational phase-field models of brittle fracture [J]. Journal of the Mechanics and Physics of Solids, 2018, 110: 80–99.MathSciNetCrossRefGoogle Scholar
  11. [11]
    BORDEN M J, HUGHES T J, LANDIS C M, et al. A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 273: 100–118.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    BORDEN M J. Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture [D]. Austin: University of Texas at Austin, 2012.Google Scholar
  13. [13]
    SARGADO J M, KEILEGAVLEN E, BERRE I, et al. High-accuracy phasefield models for brittle fracture based on a new family of degradation functions [J]. Journal of the Mechanics and Physics of Solids, 2017. https://doi.org/10.1016/j.jmps.2017.10.015 (published online).Google Scholar
  14. [14]
    AMOR H, MARIGO J J, MAURINI C. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments [J]. Journal of the Mechanics and Physics of Solids, 2009, 57: 1209–1229.CrossRefMATHGoogle Scholar
  15. [15]
    MIEHE C, WELSCHINGER F, HOFACKER M. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations [J]. International Journal for Numerical Methods in Engineering, 2010, 83: 1273–1311.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    GERASIMOV T, DE LORENZIS L. A line search assisted monolithic approach for phase-field computing of brittle fracture [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 276–303.MathSciNetCrossRefGoogle Scholar
  17. [17]
    WHEELER M, WICK T, WOLLNER W. An augmented-Lagrangian method for the phasefield approach for pressurized fractures [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 271: 69–85.MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    ZIAEI-RAD V, SHEN Y. Massive parallelization of the phase field formulation for crack propagation with time adaptivity [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 312, 224–253.MathSciNetCrossRefGoogle Scholar

Copyright information

© Shanghai Jiaotong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yongxing Shen (沈泳星)
    • 1
    • 2
  • Mostafa Mollaali
    • 1
    • 2
  • Yihuan Li (李毅环)
    • 1
    • 2
  • Weixin Ma (马维馨)
    • 1
    • 2
  • Jiahao Jiang (蒋家皓)
    • 3
  1. 1.State Key Laboratory of Metal Matrix CompositesShanghai Jiao Tong UniversityShanghaiChina
  2. 2.University of Michigan - Shanghai Jiao Tong University Joint InstituteShanghai Jiao Tong UniversityShanghaiChina
  3. 3.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA

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