SISSA Preprints

# Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity

 dc.contributor.author Focardi, Matteo dc.contributor.author Iurlano, Flaviana dc.date.accessioned 2013-05-13T12:15:50Z dc.date.available 2013-05-13T12:15:50Z dc.date.issued 2013-05 dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/6615 dc.description.abstract We provide an approximation result in the sense of $\Gamma$-convergence for en_US cohesive fracture energies of the form $\int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1},$ where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being $\int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx,$ where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$. dc.language.iso en en_US dc.publisher SISSA en_US dc.title Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity en_US dc.type Preprint en_US dc.subject.keyword Functions of bounded deformation en_US dc.subject.keyword free discontinuity problems en_US dc.subject.keyword cohesive fracture en_US dc.subject.miur MAT/05 ANALISI MATEMATICA dc.miur.area 1 en_US dc.contributor.area Mathematics en_US
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