Browsing by Author "Orlando, Gianluca"

Now showing 1 - 3 of 3
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    Cohesive fracture with irreversibility: quasistatic evolution for a model subject to fatigue
    (SISSA, 2016-07-19) Crismale, Vito; Lazzaroni, Giuliano; Orlando, Gianluca; Mathematics
    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 rst step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main di culty 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
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    Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case
    (SISSA, 2015-04) Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica; Mathematics
    We study the asymptotic behavior of a variational model for damaged elastoplastic materials in the case of antiplane shear. The energy functionals we consider depend on a small parameter " , which forces damage concentration on regions of codimension one. We determine the 􀀀-limit as " tends to zero and show that it contains an energy term involving the crack opening.
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    Lower semicontinuity of a class of integral functionals on the space of functions of bounded deformation
    (SISSA, 2015-09-24) Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica; Mathematics
    We study the lower semicontinuity of some free discontinuity functionals, whose volume term depends on the Euclidean norm of the symmetrized gradient.