Proximal Galerkin for Phase Field Fracture
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914515134709760 |
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| author | Castillón, Miguel Khara, Biswajit Dokken, Jørgen S. Surowiec, Thomas M. Keith, Brendan Bazilevs, Yuri |
| author_facet | Castillón, Miguel Khara, Biswajit Dokken, Jørgen S. Surowiec, Thomas M. Keith, Brendan Bazilevs, Yuri |
| contents | The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and boundedness of the phase-field variable. This work proposes the proximal Galerkin (PG) methodology as a robust and efficient framework for solving phase-field fracture problems. By reformulating the inequality-constrained optimization problem into a sequence of saddle-point problems involving latent variables, the PG method rigorously enforces the physical bounds of the phase-field variable and naturally handles the irreversibility condition. This approach is directly applicable to both static and dynamic phase-field fracture problems. The numerical results demonstrate that the PG framework accurately reproduces theoretical predictions and experimental observations, while offering a unified, mathematically consistent treatment of the constraints inherent to phase-field fracture modeling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26210 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proximal Galerkin for Phase Field Fracture Castillón, Miguel Khara, Biswajit Dokken, Jørgen S. Surowiec, Thomas M. Keith, Brendan Bazilevs, Yuri Numerical Analysis The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and boundedness of the phase-field variable. This work proposes the proximal Galerkin (PG) methodology as a robust and efficient framework for solving phase-field fracture problems. By reformulating the inequality-constrained optimization problem into a sequence of saddle-point problems involving latent variables, the PG method rigorously enforces the physical bounds of the phase-field variable and naturally handles the irreversibility condition. This approach is directly applicable to both static and dynamic phase-field fracture problems. The numerical results demonstrate that the PG framework accurately reproduces theoretical predictions and experimental observations, while offering a unified, mathematically consistent treatment of the constraints inherent to phase-field fracture modeling. |
| title | Proximal Galerkin for Phase Field Fracture |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.26210 |