We obtain a cohesive fracture model as a Γ-limit of scalar damage models in which the elastic coefficient is computed from the damage variable v through a function f_k of the form f_k (v) = min{1, ε_k^{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 → ∞. If the function f is allowed to depend on the index k, 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.

Phase field approximation of cohesive fracture models / Sergio, Conti; Matteo, Focardi; Flaviana, Iurlano. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - STAMPA. - 33(2016), pp. 1033-1067. [10.1016/j.anihpc.2015.02.001]

Phase field approximation of cohesive fracture models

FOCARDI, MATTEO;
2016

Abstract

We obtain a cohesive fracture model as a Γ-limit of scalar damage models in which the elastic coefficient is computed from the damage variable v through a function f_k of the form f_k (v) = min{1, ε_k^{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 → ∞. If the function f is allowed to depend on the index k, 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.
33
1033
1067
Sergio, Conti; Matteo, Focardi; Flaviana, Iurlano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/945936
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