Finite element simulation of pressure-loaded phase-field fractures

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Abstract

A non-standard aspect of phase-field fracture formulations for pressurized cracks is the application of the pressure loading, due to the fact that a direct notion of the fracture surfaces is absent. In this work we study the possibility to apply the pressure loading through a traction boundary condition on a contour of the phase field. Computationally this requires application of a surface-extraction algorithm to obtain a parametrization of the loading boundary. When the phase-field value of the loading contour is chosen adequately, the recovered loading contour resembles that of the sharp fracture problem. The computational scheme used to construct the immersed loading boundary is leveraged to propose a hybrid model. In this hybrid model the solid domain (outside the loading contour) is unaffected by the phase field, while a standard phase-field formulation is used in the fluid domain (inside the loading contour). We present a detailed study and comparison of the (Formula presented.)-convergence behavior and mesh convergence behavior of both models using a one-dimensional model problem. The extension of these results to multiple dimensions is also considered.

Original languageEnglish
Pages (from-to)1513-1545
Number of pages33
JournalMeccanica
Volume53
Issue number6
DOIs
Publication statusPublished - 2018

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simulation
formulations
traction
Boundary conditions
Cracks
mesh
Fluids
cracks
boundary conditions
fluids

Keywords

  • Brittle fracture
  • Finite cell method
  • Immersed finite element method
  • Phase-field modeling
  • Pressurized cracks

Cite this

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title = "Finite element simulation of pressure-loaded phase-field fractures",
abstract = "A non-standard aspect of phase-field fracture formulations for pressurized cracks is the application of the pressure loading, due to the fact that a direct notion of the fracture surfaces is absent. In this work we study the possibility to apply the pressure loading through a traction boundary condition on a contour of the phase field. Computationally this requires application of a surface-extraction algorithm to obtain a parametrization of the loading boundary. When the phase-field value of the loading contour is chosen adequately, the recovered loading contour resembles that of the sharp fracture problem. The computational scheme used to construct the immersed loading boundary is leveraged to propose a hybrid model. In this hybrid model the solid domain (outside the loading contour) is unaffected by the phase field, while a standard phase-field formulation is used in the fluid domain (inside the loading contour). We present a detailed study and comparison of the (Formula presented.)-convergence behavior and mesh convergence behavior of both models using a one-dimensional model problem. The extension of these results to multiple dimensions is also considered.",
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Finite element simulation of pressure-loaded phase-field fractures. / Singh, N.; Verhoosel, C.V.; van Brummelen, E.H.

In: Meccanica, Vol. 53, No. 6, 2018, p. 1513-1545.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Finite element simulation of pressure-loaded phase-field fractures

AU - Singh, N.

AU - Verhoosel, C.V.

AU - van Brummelen, E.H.

PY - 2018

Y1 - 2018

N2 - A non-standard aspect of phase-field fracture formulations for pressurized cracks is the application of the pressure loading, due to the fact that a direct notion of the fracture surfaces is absent. In this work we study the possibility to apply the pressure loading through a traction boundary condition on a contour of the phase field. Computationally this requires application of a surface-extraction algorithm to obtain a parametrization of the loading boundary. When the phase-field value of the loading contour is chosen adequately, the recovered loading contour resembles that of the sharp fracture problem. The computational scheme used to construct the immersed loading boundary is leveraged to propose a hybrid model. In this hybrid model the solid domain (outside the loading contour) is unaffected by the phase field, while a standard phase-field formulation is used in the fluid domain (inside the loading contour). We present a detailed study and comparison of the (Formula presented.)-convergence behavior and mesh convergence behavior of both models using a one-dimensional model problem. The extension of these results to multiple dimensions is also considered.

AB - A non-standard aspect of phase-field fracture formulations for pressurized cracks is the application of the pressure loading, due to the fact that a direct notion of the fracture surfaces is absent. In this work we study the possibility to apply the pressure loading through a traction boundary condition on a contour of the phase field. Computationally this requires application of a surface-extraction algorithm to obtain a parametrization of the loading boundary. When the phase-field value of the loading contour is chosen adequately, the recovered loading contour resembles that of the sharp fracture problem. The computational scheme used to construct the immersed loading boundary is leveraged to propose a hybrid model. In this hybrid model the solid domain (outside the loading contour) is unaffected by the phase field, while a standard phase-field formulation is used in the fluid domain (inside the loading contour). We present a detailed study and comparison of the (Formula presented.)-convergence behavior and mesh convergence behavior of both models using a one-dimensional model problem. The extension of these results to multiple dimensions is also considered.

KW - Brittle fracture

KW - Finite cell method

KW - Immersed finite element method

KW - Phase-field modeling

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