Vectorial, geometrically nonlinear, phase-field approximation of a cohesive fracture energy - (online)
speaker: Flaviana Iurlano (Sorbonne Université)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.
timetable:
Fri 10 Sep, 10:20 - 11:10,
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