Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929590267543552 |
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| author | Friedrich, Manuel Seutter, Joscha |
| author_facet | Friedrich, Manuel Seutter, Joscha |
| contents | We study the atomistic-to-continuum limit for a model of a quasi-static crack evolution driven by time-dependent boundary conditions. We consider a two-dimensional atomic mass spring system whose interactions are modeled by classical interaction potentials, supplemented by a suitable irreversibility condition accounting for the breaking of atmoic bonding. In a simultaneous limit of vanishing interatomic distance and discretized time step, we identify a continuum model of quasi-static crack growth in brittle fracture featuring an irreversibility condition, a global stability, and an energy balance. The proof of global stability relies on a careful adaptation of the jump-transfer argument by Francfort and Larsen to the atomistic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials Friedrich, Manuel Seutter, Joscha Analysis of PDEs 49J45, 70G75, 74A25, 74R10 We study the atomistic-to-continuum limit for a model of a quasi-static crack evolution driven by time-dependent boundary conditions. We consider a two-dimensional atomic mass spring system whose interactions are modeled by classical interaction potentials, supplemented by a suitable irreversibility condition accounting for the breaking of atmoic bonding. In a simultaneous limit of vanishing interatomic distance and discretized time step, we identify a continuum model of quasi-static crack growth in brittle fracture featuring an irreversibility condition, a global stability, and an energy balance. The proof of global stability relies on a careful adaptation of the jump-transfer argument by Francfort and Larsen to the atomistic setting. |
| title | Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials |
| topic | Analysis of PDEs 49J45, 70G75, 74A25, 74R10 |
| url | https://arxiv.org/abs/2402.02966 |