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

C. J. Larsen, J. E. Dolbow, O. Lopez-Pamies

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
JournalInternational Journal of Fracture
DOIs
StateAccepted/In press - 2024

Keywords

  • Brittle materials
  • Crack nucleation
  • Crack propagation
  • Fracture energy
  • Strength

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Mechanics of Materials

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