We present an approximation result for functions u: Ω {\textrightarrow} ℝ^n belonging to the space GSBD(Ω) ∩ L2(Ω, ℝn) with e(u) square integrable and Hn-1(Ju) finite. The approximating functions uk are piecewise continuous functions such that uk {\textrightarrow} u in (Formula Presented). As an application, we provide the extension to the vector-valued case of the Γ-convergence result in GSBV(Ω) proved by Ambrosio and Tortorelli (Commun Pure Appl Math 43:999-1036, 1990; Boll. Un. Mat. Ital. B (7) 6:105-123, 1992).

}, doi = {10.1007/s00526-013-0676-7}, url = {http://urania.sissa.it/xmlui/handle/1963/34647}, author = {Flaviana Iurlano} } @article {2013, title = {Ambrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity}, year = {2013}, institution = {SISSA}, abstract = {We provide an approximation result in the sense of $\Gamma$-convergence for 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{\textquoteright}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 $\gamma\>0$.

}, keywords = {Functions of bounded deformation}, url = {http://hdl.handle.net/1963/6615}, author = {Matteo Focardi and Flaviana Iurlano} } @mastersthesis {2013, title = {An Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems}, year = {2013}, school = {SISSA}, keywords = {Functions of bounded deformation}, author = {Flaviana Iurlano} } @article {2013, title = {Fracture models as Gamma-limits of damage models}, journal = {Communications on Pure and Applied Analysis 12 (2013) 1657-1686}, number = {SISSA;25/2011/M}, year = {2013}, publisher = {American Institute of Mathematical Sciences}, abstract = {We analyze the asymptotic behavior of a variational model for damaged elastic materials. This model depends on two small parameters, which govern the width of the damaged regions and the minimum elasticity constant attained in the damaged regions. When these parameters tend to zero, we find that the corresponding functionals Gamma-converge to a functional related to fracture mechanics. The corresponding problem is brittle or cohesive, depending on the asymptotic ratio of the two parameters.

}, doi = {10.3934/cpaa.2013.12.1657}, url = {http://hdl.handle.net/1963/4225}, author = {Gianni Dal Maso and Flaviana Iurlano} } @article {10226, title = {Fracture and plastic models as Gamma-limits of damage models under different regimes}, journal = {Advances in Calculus of Variations., to appear.}, number = {SISSA;59/2011/M}, year = {2011}, publisher = {Walter de Gruyter}, abstract = {We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Gamma-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

}, doi = {10.1515/acv-2011-0011}, url = {http://hdl.handle.net/1963/5069}, author = {Flaviana Iurlano} } @mastersthesis {2010, title = {New approximation results for free discontinuity problems}, year = {2010}, type = {Master{\textquoteright}s thesis}, author = {Flaviana Iurlano} }