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

2024/01/25 by Larsen, C. J., Dolbow, J. E., Lopez-Pamies, O. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)

paper · doi:10.48550/arxiv.2401.13938

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.

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