Phase field approximation of cohesive fracture models

We obtain a cohesive fracture model as Gamma-limit epsilon -> 0, of scalar damage models in which the elastic coefficient is computed from the damage variable v through a function f(epsilon) of the form f(epsilon)(v) = min{1, epsilon(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 -> infinity. If in addition the function f is allowed to depend on the parameter epsilon, 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. (C) 2015 Elsevier Masson SAS. All rights reserved.