Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation
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arXiv
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866908573833887744 |
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| author | Caponi, Maicol |
| author_facet | Caponi, Maicol |
| contents | We propose a phase-field model of dynamic fracture based on the Ambrosio--Tortorelli's approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in [C.J. Larsen, C. Ortner, and E. Süli, Math. Models Methods Appl. Sci. (2010)], we show the existence of a dynamic crack evolution satisfying an energy-dissipation balance, according to Griffith's criterion. Finally, we analyze the dynamic phase-field model of [B. Bourdin, C.J. Larsen, and C.L. Richardson, Int. J. Fracture (2011)] and [C.J. Larsen, IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials (2010)] with no dissipative terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_01986 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation Caponi, Maicol Analysis of PDEs 35L53, 35Q74, 49J40, 74R10 We propose a phase-field model of dynamic fracture based on the Ambrosio--Tortorelli's approximation, which takes into account dissipative effects due to the speed of the crack tips. By adapting the time discretization scheme contained in [C.J. Larsen, C. Ortner, and E. Süli, Math. Models Methods Appl. Sci. (2010)], we show the existence of a dynamic crack evolution satisfying an energy-dissipation balance, according to Griffith's criterion. Finally, we analyze the dynamic phase-field model of [B. Bourdin, C.J. Larsen, and C.L. Richardson, Int. J. Fracture (2011)] and [C.J. Larsen, IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials (2010)] with no dissipative terms. |
| title | Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation |
| topic | Analysis of PDEs 35L53, 35Q74, 49J40, 74R10 |
| url | https://arxiv.org/abs/1908.01986 |