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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2507.12169 |
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| _version_ | 1866911202190295040 |
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| author | Alessi, Roberto Colasanto, Francesco Focardi, Matteo |
| author_facet | Alessi, Roberto Colasanto, Francesco Focardi, Matteo |
| contents | The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture.
In this first paper we establish the mathematical foundation of a cohesive phase-field model by proving a $Γ$-convergence result in a one-dimensional setting. Specifically, we consider a broad class of phase-field energies, encompassing different models present in the literature, thereby both extending the results in \cite{ContiFocardiIurlano2016} and providing an analytical validation of all the other approaches. Additionally, by modifying the functional scaling, we demonstrate that our formulation also generalizes the Ambrosio-Tortorelli approximation for brittle fracture, therefore laying the groundwork for a unified framework for variational fracture problems.
The Part~II paper presents a systematic procedure for constructing phase-field models that reproduce prescribed cohesive laws, whereas the Part~III paper validates the theoretical results with applied examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12169 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase-field modelling of cohesive fracture. Part I: $Γ$-convergence results Alessi, Roberto Colasanto, Francesco Focardi, Matteo Analysis of PDEs The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture. In this first paper we establish the mathematical foundation of a cohesive phase-field model by proving a $Γ$-convergence result in a one-dimensional setting. Specifically, we consider a broad class of phase-field energies, encompassing different models present in the literature, thereby both extending the results in \cite{ContiFocardiIurlano2016} and providing an analytical validation of all the other approaches. Additionally, by modifying the functional scaling, we demonstrate that our formulation also generalizes the Ambrosio-Tortorelli approximation for brittle fracture, therefore laying the groundwork for a unified framework for variational fracture problems. The Part~II paper presents a systematic procedure for constructing phase-field models that reproduce prescribed cohesive laws, whereas the Part~III paper validates the theoretical results with applied examples. |
| title | Phase-field modelling of cohesive fracture. Part I: $Γ$-convergence results |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.12169 |