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]
Titolo: | Phase field approximation of cohesive fracture models | |
Autori di Ateneo: | ||
Autori: | Sergio, Conti; FOCARDI, MATTEO; Flaviana, Iurlano | |
Anno di registrazione: | 2016 | |
Rivista: | ||
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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