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Quasi-static crack propagation by Griffith's criterion
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Negri, Matteo and Ortner, Christoph (2008) Quasi-static crack propagation by Griffith's criterion. Mathematical Models and Methods in Applied Sciences, Volume 18 (Number 11). pp. 1895-1925. doi:10.1142/S0218202508003236 ISSN 0218-2025.
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Official URL: http://dx.doi.org/10.1142/S0218202508003236
Abstract
We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith's criterion in a suitable form which takes into account both stable and unstable propagations, as well as an energy balance formula which accounts for dissipation in the unstable regime. If the load is monotonically increasing, this solution is explicit and almost everywhere unique. For more general loads we construct a solution via time discretization. Finally, we consider a finite element discretization of the problem and prove convergence of the discrete solutions.
| Item Type: | Journal Article | ||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Fracture mechanics, Brittleness -- Mathematical models | ||||
| Journal or Publication Title: | Mathematical Models and Methods in Applied Sciences | ||||
| Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
| ISSN: | 0218-2025 | ||||
| Official Date: | November 2008 | ||||
| Dates: |
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| Volume: | Volume 18 | ||||
| Number: | Number 11 | ||||
| Page Range: | pp. 1895-1925 | ||||
| DOI: | 10.1142/S0218202508003236 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 20 December 2015 | ||||
| Date of first compliant Open Access: | 20 December 2015 | ||||
| Funder: | Fifth Framework Programme (European Commission) (FP5) | ||||
| Grant number: | HPRN-CT-2002-00284 (FP5) |
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