Phase field approximation of cohesive fracture models

By Sergio Conti, Matteo Focardi, Flaviana Iurlano. 2014

138 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ecb28c3522b493953c71c1b629c2196c45fa7948

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In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Representative works in this direction includes the modeling of brittle fracture [63, 119, 326].”
Crack nucleation in variational phase-field models of brittle fracture (2018, unknown): “They have been expended to account for dynamic eﬀects, ductile behavior [2, 71, 3], cohesive eﬀects [33, 32, 42], large deformations [4, 70, 14], or anisotropy [63], for instance.”
Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples (2017, unknown): “References [29] and [39] recently proposed an alternative interesting phase-field model of cohesive fracture without introducing plastic effects.”
Revisiting nucleation in the phase-field approach to brittle fracture (2020, background): “While there remain theoretical and practical issues yet to be addressed, some progress has been recently made on that front; see, e.g., Conti et al. (2016) , Focardi and Iurlano (2017) , and Wu and Nguyen (2018) .”