Abstract
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 (u,v) defined by the PDEs for the displacement field u and the phase field v is shown to correspond to the fields that minimize separately two different functionals, much like the solution pair (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.
Original language | English (US) |
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Pages (from-to) | 319-327 |
Number of pages | 9 |
Journal | International Journal of Fracture |
Volume | 247 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2024 |
Keywords
- Brittle materials
- Crack nucleation
- Crack propagation
- Fracture energy
- Strength
ASJC Scopus subject areas
- Computational Mechanics
- Modeling and Simulation
- Mechanics of Materials