01651nas a2200145   4500008004100000245009700041210006900138300001400207490000700221520116600228100001901394700002401413700002201437856004601459       2018                        eng d00aCohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue0 aCohesive fracture with irreversibility Quasistatic evolution for  a1371-14120 v283 a<p>In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.</p>1 aCrismale, Vito1 aLazzaroni, Giuliano1 aOrlando, Gianluca  uhttps://doi.org/10.1142/S021820251850037900974nas a2200121   4500008004300000245009300043210006900136260004800205520051800253100002100771700002400792856003600816       2011                        en_Ud  00aCrack growth with non-interpenetration : a simplified proof for the pure Neumann problem0 aCrack growth with noninterpenetration a simplified proof for the  bAmerican Institute of Mathematical Sciences3 aWe present a recent existence result concerning the quasi-static evolution of cracks in hyperelastic brittle materials, in the frame-work of finite elasticity with non-interpenetration. In particular, here we consider the problem where no Dirichlet conditions are imposed, the boundary is traction-free, and the body is subject only to time-dependent volume forces. This allows us to present the main ideas of the proof in a simpler way, avoiding some of the technicalities needed in the general case, studied in.1 aDal Maso, Gianni1 aLazzaroni, Giuliano  uhttp://hdl.handle.net/1963/3801