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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.22072 |
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| _version_ | 1866918107324350464 |
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| author | Alessi, Roberto Colasanto, Francesco Focardi, Matteo |
| author_facet | Alessi, Roberto Colasanto, Francesco Focardi, Matteo |
| contents | This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical foundations established in the first two parts, which included a $Γ$-convergence result for a broad class of phase-field energy functionals and the presentation of a rigorous analytical methodology for constructing models tailored to specific cohesive laws, this third paper explores the mechanical response of phase-field models, most of which are novel, associated with different cohesive fracture behaviors within a one-dimensional framework. Particular emphasis is placed on the possibility of formulating distinct phase-field models that, despite exhibiting different evolutions of their phase-field and displacement profiles, yield identical cohesive fracture responses. Thus, this work aims at providing a practical interpretation of the mathematical framework connecting the theoretical insights established in the previous parts for physical relevant applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application Alessi, Roberto Colasanto, Francesco Focardi, Matteo Analysis of PDEs Materials Science This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical foundations established in the first two parts, which included a $Γ$-convergence result for a broad class of phase-field energy functionals and the presentation of a rigorous analytical methodology for constructing models tailored to specific cohesive laws, this third paper explores the mechanical response of phase-field models, most of which are novel, associated with different cohesive fracture behaviors within a one-dimensional framework. Particular emphasis is placed on the possibility of formulating distinct phase-field models that, despite exhibiting different evolutions of their phase-field and displacement profiles, yield identical cohesive fracture responses. Thus, this work aims at providing a practical interpretation of the mathematical framework connecting the theoretical insights established in the previous parts for physical relevant applications. |
| title | Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering application |
| topic | Analysis of PDEs Materials Science |
| url | https://arxiv.org/abs/2507.22072 |