A variational formulation of Griffith phase-field fracture with material strength
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913208983355392 |
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| author | Larsen, C. J. Dolbow, J. E. Lopez-Pamies, O. |
| author_facet | Larsen, C. J. Dolbow, J. E. Lopez-Pamies, O. |
| contents | In this expository Note, it is shown that the Griffith phase-field theory of fracture accounting for material strength originally introduced by Kumar, Francfort, and Lopez-Pamies (J Mech Phys Solids 112, 523--551, 2018) in the form of PDEs can be recast as a variational theory. In particular, the solution pair $(\textbf{u},v)$ defined by the PDEs for the displacement field $\textbf{u}$ and the phase field $v$ is shown to correspond to the fields that minimize separately two different functionals, much like the solution pair $(\textbf{u},v)$ defined by the original phase-field theory of fracture without material strength implemented in terms of alternating minimization. The merits of formulating a complete theory of fracture nucleation and propagation via such a variational approach -- in terms of the minimization of two different functionals -- are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_13938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A variational formulation of Griffith phase-field fracture with material strength Larsen, C. J. Dolbow, J. E. Lopez-Pamies, O. Analysis of PDEs Materials Science In this expository Note, it is shown that the Griffith phase-field theory of fracture accounting for material strength originally introduced by Kumar, Francfort, and Lopez-Pamies (J Mech Phys Solids 112, 523--551, 2018) in the form of PDEs can be recast as a variational theory. In particular, the solution pair $(\textbf{u},v)$ defined by the PDEs for the displacement field $\textbf{u}$ and the phase field $v$ is shown to correspond to the fields that minimize separately two different functionals, much like the solution pair $(\textbf{u},v)$ defined by the original phase-field theory of fracture without material strength implemented in terms of alternating minimization. The merits of formulating a complete theory of fracture nucleation and propagation via such a variational approach -- in terms of the minimization of two different functionals -- are discussed. |
| title | A variational formulation of Griffith phase-field fracture with material strength |
| topic | Analysis of PDEs Materials Science |
| url | https://arxiv.org/abs/2401.13938 |