Finite element simulation of pressure-loaded phase-field fractures

Finite element simulation of pressure-loaded phase-field fractures 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 $$\varGamma$$ Γ -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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Meccanica Springer Journals

Finite element simulation of pressure-loaded phase-field fractures

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Publisher
Springer Netherlands
Copyright
Copyright © 2017 by The Author(s)
Subject
Physics; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering
ISSN
0025-6455
eISSN
1572-9648
D.O.I.
10.1007/s11012-017-0802-2
Publisher site
See Article on Publisher Site

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 $$\varGamma$$ Γ -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.

Journal

MeccanicaSpringer Journals

Published: Dec 12, 2017

References

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