Chen, L., Li, B. and de Borst, R. (2020) Adaptive isogeometric analysis for phase‐field modeling of anisotropic brittle fracture. International Journal for Numerical Methods in Engineering, 121 (20). pp. 4630-4648. ISSN 0029-5981
Abstract
The surface energy a phase‐field approach to brittle fracture in anisotropic materials is also anisotropic and gives rise to second‐order gradients in the phase field entering the energy functional. This necessitates C 1 continuity of the basis functions which are used to interpolate the phase field. The basis functions which are employed in isogeometric analysis (IGA), such as nonuniform rational B‐splines and T‐splines naturally possess a higher order continuity and are therefore ideally suited for phase‐field models which are equipped with an anisotropic surface energy. Moreover, the high accuracy of spline discretizations, also relative to their computational demand, significantly reduces the fineness of the required discretization. This holds a fortiori if adaptivity is included. Herein, we present two adaptive refinement schemes in IGA, namely, adaptive local refinement and adaptive hierarchical refinement, for phase‐field simulations of anisotropic brittle fracture. The refinement is carried out using a subdivision operator and exploits the Bézier extraction operator. Illustrative examples are included, which show that the method can simulate highly complex crack patterns such as zigzag crack propagation. An excellent agreement is obtained between the solutions from global refinement and adaptive refinement, with a reasonable reduction of the computational effort when using adaptivity.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 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: | Phase-field; anisotropic surface energy; isogeometric analysis; T-splines; adaptivity |
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: | 05 Aug 2020 12:14 |
Last Modified: | 21 Jan 2022 14:06 |
Status: | Published |
Publisher: | Wiley |
Refereed: | Yes |
Identification Number: | 10.1002/nme.6457 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:164059 |