01521nas a2200133   4500008004100000245009100041210006900132260001000201520106100211653003701272100002001309700002201329856003601351       2013                        en  d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in   bSISSA3 a<p>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'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 $\gamma&gt;0$.</p>10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana  uhttp://hdl.handle.net/1963/661500531nas a2200109   4500008004100000245011300041210006900154260001000223653003700233100002200270856012900292       2013                        en  d00aAn Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems0 aApproximation Result for Generalised Functions of Bounded Deform  bSISSA10aFunctions of bounded deformation1 aIurlano, Flaviana  uhttps://www.math.sissa.it/publication/approximation-result-generalised-functions-bounded-deformation-and-applications-damage