Chen, L., Li, B. and de Borst, R. orcid.org/0000-0002-3457-3574 (2021) The use of Powell-Sabin B-Splines in a higher-order phase-field model for crack kinking. Computational Mechanics, 67 (1). pp. 127-137. ISSN 0178-7675
Abstract
Phase-field models for brittle fracture in anisotropic materials result in a fourth-order partial differential equation for the damage evolution. This necessitates a C1 continuity of the basis functions. Here, Powell-Sabin B-splines, which are based on triangles, are used for the approximation of the field variables as well as for the the description of the geometry. The use of triangles makes adaptive mesh refinement and discrete crack insertion straightforward. Bézier extraction is used to cast the B-splines in a standard finite element format. A procedure to impose Dirichlet boundary condition is provided for these elements. The versatility and accuracy of the approach are assessed in two case studies, featuring crack kinking and zig-zag crack propagation. It is also shown that the adaptive refinement well captures the evolution of the phase field.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer-Verlag GmbH Germany, part of Springer Nature 2020. This is an author-produced version of a paper subsequently published in Computational Mechanics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Phase-field model; Powell-Sabin B-splines; Anisotropy; Bézier extraction; Adaptive refinement |
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: | 25 Sep 2020 08:23 |
Last Modified: | 26 Jan 2022 16:35 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s00466-020-01923-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:165923 |