Phase field approximation of cohesive fracture models

Sergio, Conti; Focardi, Matteo; Flaviana, Iurlano

doi:10.1016/j.anihpc.2015.02.001

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.

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Titolo:	Phase field approximation of cohesive fracture models
Autori di Ateneo:	Sergio, Conti FOCARDI, MATTEO Flaviana, Iurlano mostra contributor esterni nascondi contributor esterni
Autori:	Sergio, Conti; FOCARDI, MATTEO; Flaviana, Iurlano
Anno di registrazione:	2016
Rivista:	ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE
Volume:	33
Pagina iniziale:	1033
Pagina finale:	1067
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.
Handle:	http://hdl.handle.net/2158/945936
Appare nelle tipologie:	1a - Articolo su rivista

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