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Analysis of cell size effects in atomistic crack propagation
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Buze, Maciej, Hudson, Thomas E. (Edward) and Ortner, Christoph (2020) Analysis of cell size effects in atomistic crack propagation. ESAIM: Mathematical Modelling and Numerical Analysis, 54 (6). pp. 1821-1847. doi:10.1051/m2an/2020005
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WRAP-analysis-cell-size-effects-atomistic-crack-propation-Ortner-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1037Kb) | Preview |
Official URL: https://doi.org/10.1051/m2an/2020005
Abstract
We consider crack propagation in a crystalline material in terms of bifurcation analysis. We provide evidence that the stress intensity factor is a natural bifurcation parameter, and that the resulting bifurcation diagram is a periodic "snaking curve". We then prove qualitative properties of the equilibria and convergence rates of finite-cell approximations to the "exact" bifurcation diagram.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics Q Science > QD Chemistry |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Crystal lattices -- Mathematical models, Bifurcation theory | ||||||||||||
| Journal or Publication Title: | ESAIM: Mathematical Modelling and Numerical Analysis | ||||||||||||
| Publisher: | EDP Sciences | ||||||||||||
| ISSN: | 0764-583X | ||||||||||||
| Official Date: | November 2020 | ||||||||||||
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| Volume: | 54 | ||||||||||||
| Number: | 6 | ||||||||||||
| Page Range: | pp. 1821-1847 | ||||||||||||
| DOI: | 10.1051/m2an/2020005 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Reuse Statement (publisher, data, author rights): | “Reproduced with permission from EDP Sciences" | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
| Copyright Holders: | © EDP Sciences, SMAI 2020 | ||||||||||||
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