A variational formulation of Griffith phase-field fracture with material strength

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 sol...

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Bibliographic Details
Published inInternational journal of fracture Vol. 247; no. 3; pp. 319 - 327
Main Authors Larsen, C. J., Dolbow, J. E., Lopez-Pamies, O.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2024
Springer Nature B.V
Subjects
Automotive Engineering
Characterization and Evaluation of Materials
Civil Engineering
Classical Mechanics
Crack propagation
Energy
Engineering
Field theory
Mechanical Engineering
Nucleation
Optimization
Partial differential equations
Propagation
Stress state
Crack nucleation
Fracture energy
Brittle materials
Strength
Crack propagation
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Summary: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.
ISSN:0376-9429
1573-2673
DOI:10.1007/s10704-024-00786-3