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

Publication ,  Journal Article
Larsen, CJ; Dolbow, JE; Lopez-Pamies, O
Published in: International Journal of Fracture
January 1, 2024

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.

Duke Scholars

Published In

International Journal of Fracture

DOI

EISSN

1573-2673

ISSN

0376-9429

Publication Date

January 1, 2024

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4017 Mechanical engineering
  • 4016 Materials engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0912 Materials Engineering
  • 0905 Civil Engineering
 

Citation

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Larsen, C. J., Dolbow, J. E., & Lopez-Pamies, O. (2024). A variational formulation of Griffith phase-field fracture with material strength. International Journal of Fracture. https://doi.org/10.1007/s10704-024-00786-3
Larsen, C. J., J. E. Dolbow, and O. Lopez-Pamies. “A variational formulation of Griffith phase-field fracture with material strength.” International Journal of Fracture, January 1, 2024. https://doi.org/10.1007/s10704-024-00786-3.
Larsen CJ, Dolbow JE, Lopez-Pamies O. A variational formulation of Griffith phase-field fracture with material strength. International Journal of Fracture. 2024 Jan 1;
Larsen, C. J., et al. “A variational formulation of Griffith phase-field fracture with material strength.” International Journal of Fracture, Jan. 2024. Scopus, doi:10.1007/s10704-024-00786-3.
Larsen CJ, Dolbow JE, Lopez-Pamies O. A variational formulation of Griffith phase-field fracture with material strength. International Journal of Fracture. 2024 Jan 1;
Journal cover image

Published In

International Journal of Fracture

DOI

EISSN

1573-2673

ISSN

0376-9429

Publication Date

January 1, 2024

Related Subject Headings

  • Mechanical Engineering & Transports
  • 4017 Mechanical engineering
  • 4016 Materials engineering
  • 4005 Civil engineering
  • 0913 Mechanical Engineering
  • 0912 Materials Engineering
  • 0905 Civil Engineering