%0 Report
%D 2018
%T Energy-dissipation balance of a smooth moving crack
%A Maicol Caponi
%A Ilaria Lucardesi
%A Emanuele Tasso
%X In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.
%G en
%U http://preprints.sissa.it/handle/1963/35320
%1 35630
%2 Mathematics
%4 1
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-08-01T09:36:30Z
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%0 Journal Article
%D 2016
%T Confinement of dislocations inside a crystal with a prescribed external strain
%A Ilaria Lucardesi
%A Marco Morandotti
%A Riccardo Scala
%A Davide Zucco
%X We study screw dislocations in an isotropic crystal undergoing antiplane shear. In the framework of linear elasticity, by fixing a suitable boundary condition for the strain (prescribed non-vanishing boundary integral), we manage to confine the dislocations inside the material. More precisely, in the presence of an external strain with circulation equal to n times the lattice spacing, it is energetically convenient to have n distinct dislocations lying inside the crystal. The novelty of introducing a Dirichlet boundary condition for the tangential strain is crucial to the confinement: it is well known that, if Neumann boundary conditions are imposed, the dislocations tend to migrate to the boundary. The results are achieved using PDE techniques and Ƭ-convergence theory, in the framework of the so-called core radius approach.
%G en
%U http://urania.sissa.it/xmlui/handle/1963/35247
%1 35558
%2 Mathematics
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2016-10-20T11:44:46Z
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%0 Report
%D 2015
%T The wave equation on domains with cracks growing on a prescribed path: existence, uniqueness, and continuous dependence on the data
%A Gianni Dal Maso
%A Ilaria Lucardesi
%X Given a bounded open set $\Omega \subset \mathbb R^d$ with Lipschitz boundary and an increasing family $\Gamma_t$, $t\in [0,T]$, of closed subsets of $\Omega$, we analyze the scalar wave equation $\ddot{u} - div (A \nabla u) = f$ in the time varying cracked domains $\Omega\setminus\Gamma_t$. Here we assume that the sets $\Gamma_t$ are contained into a prescribed $(d-1)$-manifold of class $C^2$. Our approach relies on a change of variables: recasting the problem on the reference configuration $\Omega\setminus \Gamma_0$, we are led to consider a hyperbolic problem of the form $\ddot{v} - div (B\nabla v) + a \cdot \nabla v - 2 b \cdot \nabla \dot{v} = g$ in $\Omega \setminus \Gamma_0$. Under suitable assumptions on the regularity of the change of variables that transforms $\Omega\setminus \Gamma_t$ into $\Omega\setminus \Gamma_0$, we prove existence and uniqueness of weak solutions for both formulations. Moreover, we provide an energy equality, which gives, as a by-product, the continuous dependence of the solutions with respect to the cracks.
%G en
%U http://urania.sissa.it/xmlui/handle/1963/34629
%1 34832
%2 Mathematics
%4 1
%# MAT/05
%$ Submitted by lucardes@sissa.it (lucardes@sissa.it) on 2015-10-12T09:08:37Z
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