Phase field approximation of cohesive fracture models
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1033-1067.

We obtain a cohesive fracture model as Γ-limit, as ε→0, of scalar damage models in which the elastic coefficient is computed from the damage variable v through a function fε of the form fε(v)=min⁡{1,ε12f(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→∞. 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.

DOI : 10.1016/j.anihpc.2015.02.001
Classification : 49J45, 26B30, 74R10, 35A35
Mots-clés : Cohesive fracture, Phase field models, Γ-convergence, Damage problems 
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     title = {Phase field approximation of cohesive fracture models},
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     pages = {1033--1067},
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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. http://www.numdam.org/articles/10.1016/j.anihpc.2015.02.001/

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