Chen, L. and de Borst, R. (2021) Weak imposition of Dirichlet boundary conditions for analyses using Powell–Sabin B‐splines. International Journal for Numerical Methods in Engineering, 122 (23). pp. 6888-6904. ISSN 0029-5981
Abstract
Powell–Sabin B-splines are enjoying an increased use in the analysis of solids and fluids, including fracture propagation. However, the Powell–Sabin B-spline interpolation does not hold the Kronecker delta property and, therefore, the imposition of Dirichlet boundary conditions is not as straightforward as for the standard finite elements. Herein, we discuss the applicability of various approaches developed to date for the weak imposition of Dirichlet boundary conditions in analyses which employ Powell–Sabin B-splines. We take elasticity and fracture propagation using phase-field modeling as a benchmark problem. We first succinctly recapitulate the phase-field model for propagation of brittle fracture, which encapsulates linear elasticity, and its discretization using Powell–Sabin B-splines. As baseline solution we impose Dirichlet boundary conditions in a strong sense, and use this to benchmark the Lagrange multiplier, penalty, and Nitsche's methods, as well as methods based on the Hellinger-Reissner principle, and the linked Lagrange multiplier method and its modified version.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 John Wiley & Sons Ltd. This is an author-produced version of a paper subsequently published in International Journal for Numerical Methods in Engineering. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Dirichlet boundary conditions; Powell-Sabin B-splines; weak imposition; fracture |
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: | 04 Jan 2022 10:24 |
Last Modified: | 31 Aug 2022 00:13 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/nme.6815 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:181918 |