We obtain a cohesive fracture model as a Gamma-limit of damage models.
In these models the elastic coefficient is computed from the damage variable v
through a function f_k of the form f_k(t)=min(1,\eps_k^{1/2} f(t)), with f
diverging for v close to the value describing undamaged material. The resulting
fracture energy is linear in the opening s at small values of s and has a finite
limit as s tends to infinity. Moreover it can be determined by solving a
one-dimensional vectorial optimal profile problem.