Eigenfracture approximation of quasi-static crack growth in brittle materials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918334333714432 |
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| author | Duong, Ba Duc Friedrich, Manuel |
| author_facet | Duong, Ba Duc Friedrich, Manuel |
| contents | We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the displacement field and an eigendeformation field that approximates the crack in the material. By imposing a suitable irreversibility condition and adopting an incremental minimization scheme, we define a notion of quasi-static evolution for this model. We then show that, as $\varepsilon \to 0$, these evolutions converge to a quasi-static crack evolution for the Griffith energy of brittle fracture, characterized by irreversibility, global stability, and an energy balance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenfracture approximation of quasi-static crack growth in brittle materials Duong, Ba Duc Friedrich, Manuel Analysis of PDEs We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the displacement field and an eigendeformation field that approximates the crack in the material. By imposing a suitable irreversibility condition and adopting an incremental minimization scheme, we define a notion of quasi-static evolution for this model. We then show that, as $\varepsilon \to 0$, these evolutions converge to a quasi-static crack evolution for the Griffith energy of brittle fracture, characterized by irreversibility, global stability, and an energy balance. |
| title | Eigenfracture approximation of quasi-static crack growth in brittle materials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.11915 |