10 sep 2021 -- 10:20 [open in google calendar]

**Abstract.**

We pursue the study started in Conti--Focardi--Iurlano '16, where a cohesive fracture model, depending on scalar-valued displacements, was obtained as $\Gamma$-limit of phase-field damage models. We focus here on the case in which the displacement variable is vector-valued. Precisely, we obtain a geometrically nonlinear cohesive fracture model as $\Gamma$-limit, as $\varepsilon\to0$, of phase-field models in which the elastic coefficient is computed from the damage variable $v$ through the function $f_\varepsilon(v):=\mathrm{min}\{1,\varepsilon^{\frac{1}{2}} f(v)\}$, with $f$ diverging for $v$ close to the value describing undamaged material. The resulting fracture energy, depending on the opening $z$ of the jump set and on the normal vector $\nu$ to the jump set, is given in terms of an asymptotic n-dimensional cell formula. It is one-homogeneous in the opening $z$ at small values of $

z

$ and has a finite limit as $

z

\to\infty$. This is a joint work with S. Conti and M. Focardi.