Phase field approximation of cohesive fracture models

Conti, S.; Focardi, M.; Iurlano, F.

doi:10.1016/j.anihpc.2015.02.001

Conti, S. ; Focardi, M. ; Iurlano, F.

Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1033-1067

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Résumé

We obtain a cohesive fracture model as Γ-limit, as $ε \to 0$ , of scalar damage models in which the elastic coefficient is computed from the damage variable v through a function $f_{ε}$ of the form $f_{ε} (v) = \min {1, ε^{\frac{1}{2}} f (v)}$ , with f diverging for v close to the value describing undamaged material. The resulting fracture energy can be determined by solving a one-dimensional vectorial optimal profile problem. It is linear in the opening s at small values of s and has a finite limit as $s \to \infty$ . If in addition the function f is allowed to depend on the parameter ε, for specific choices we recover in the limit Dugdale's and Griffith's fracture models, and models with surface energy density having a power-law growth at small openings.

MR Zbl

DOI : 10.1016/j.anihpc.2015.02.001

Classification : 49J45, 26B30, 74R10, 35A35
Keywords: Cohesive fracture, Phase field models, Γ-convergence, Damage problems

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     author = {Conti, S. and Focardi, M. and Iurlano, F.},
     title = {Phase field approximation of cohesive fracture models},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1033--1067},
     year = {2016},
     publisher = {Elsevier},
     volume = {33},
     number = {4},
     doi = {10.1016/j.anihpc.2015.02.001},
     mrnumber = {3519531},
     zbl = {1345.49012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2015.02.001/}
}

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Conti, S.; Focardi, M.; Iurlano, F. Phase field approximation of cohesive fracture models. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1033-1067. doi: 10.1016/j.anihpc.2015.02.001

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