Phase field approximation of cohesive fracture models

Sergio Conti; Matteo Focardi; Flaviana Iurlano

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arXiv · 1405.6883

Phase field approximation of cohesive fracture models

Sergio Conti·Matteo Focardi·Flaviana Iurlano

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Abstract

We obtain a cohesive fracture model as a $\Gamma$-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 $f_k(v)=min\{1,\varepsilon_k^{1/2} f(v)\}$, 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 $s\to\infty$. 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.

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Sergio Conti, Matteo Focardi, Flaviana Iurlano. 2014-05-27. Phase field approximation of cohesive fracture models. https://arxiv.org/abs/1405.6883

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