An optimization‐based phase‐field method for continuous‐discontinuous crack propagation
Abstract
Summary A new continuous‐discontinuous strategy for the computational modeling of crack propagation within the context of phase‐field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase‐field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two‐dimensional quasi‐static fracture mechanics are presented to demonstrate the accuracy and robustness of the method.
- Authors:
-
[3];
- Department of Mechanical Engineering and Materials Science Duke University Durham North Carolina
- Department of Civil and Environmental Engineering Duke University Durham North Carolina
- Department of Mechanical Engineering and Materials Science Duke University Durham North Carolina, Department of Civil and Environmental Engineering Duke University Durham North Carolina
- Laboratori de Càlcul Numèric (LaCàN) Universitat Politècnica de Catalunya, BarcelonaTech Barcelona Spain
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1461701
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- International Journal for Numerical Methods in Engineering
- Additional Journal Information:
- Journal Name: International Journal for Numerical Methods in Engineering Journal Volume: 116 Journal Issue: 1; Journal ID: ISSN 0029-5981
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Geelen, Rudy J. M., Liu, Yingjie, Dolbow, John E., and Rodríguez-Ferran, Antonio. An optimization‐based phase‐field method for continuous‐discontinuous crack propagation. United Kingdom: N. p., 2018.
Web. doi:10.1002/nme.5911.
Geelen, Rudy J. M., Liu, Yingjie, Dolbow, John E., & Rodríguez-Ferran, Antonio. An optimization‐based phase‐field method for continuous‐discontinuous crack propagation. United Kingdom. https://doi.org/10.1002/nme.5911
Geelen, Rudy J. M., Liu, Yingjie, Dolbow, John E., and Rodríguez-Ferran, Antonio. Wed .
"An optimization‐based phase‐field method for continuous‐discontinuous crack propagation". United Kingdom. https://doi.org/10.1002/nme.5911.
@article{osti_1461701,
title = {An optimization‐based phase‐field method for continuous‐discontinuous crack propagation},
author = {Geelen, Rudy J. M. and Liu, Yingjie and Dolbow, John E. and Rodríguez-Ferran, Antonio},
abstractNote = {Summary A new continuous‐discontinuous strategy for the computational modeling of crack propagation within the context of phase‐field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase‐field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two‐dimensional quasi‐static fracture mechanics are presented to demonstrate the accuracy and robustness of the method.},
doi = {10.1002/nme.5911},
journal = {International Journal for Numerical Methods in Engineering},
number = 1,
volume = 116,
place = {United Kingdom},
year = {Wed Jul 25 00:00:00 EDT 2018},
month = {Wed Jul 25 00:00:00 EDT 2018}
}
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