Linse, T., Hennig, P., Kaestner, M. et al. (1 more author) (2017) A convergence study of phase-field models for brittle fracture. Engineering Fracture Mechanics, 184. pp. 307-318. ISSN 0013-7944
Abstract
A crucial issue in phase-field models for brittle fracture is whether the functional that describes the distributed crack converges to the functional of the discrete crack when the internal length scale introduced in the distribution function goes to zero. Theoretical proofs exist for the original theory. However, for continuous media as well as for discretised media, significant errors have been reported in numerical solutions regarding the approximated crack surface, and hence for the dissipated energy. We show that for a practical setting, where the internal length scale and the spacing of the discretisation are small but finite, the observed discrepancy partially stems from the fact that numerical studies consider specimens of a finite length, and partially relates to the irreversibility introduced when casting the variational theory for brittle fracture in a damage-like format. While some form of irreversibility may be required in numerical implementations, the precise form significantly influences the accuracy and convergence towards the discrete crack.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Elsevier. This is an author produced version of a paper subsequently published in Engineering Fracture Mechanics. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Phase-field model; Fracture; Damage; Gamma convergence |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Funding Information: | Funder Grant number EUROPEAN COMMISSION - HORIZON 2020 664734 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Sep 2017 14:58 |
Last Modified: | 12 Sep 2018 00:38 |
Published Version: | https://doi.org/10.1016/j.engfracmech.2017.09.013 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.engfracmech.2017.09.013 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:121124 |