Browsing by Author "Crismale, Vito"

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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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    Globally stable quasi static evolution for strain gradient plasticity coupled with damage
    (2015) Crismale, Vito; ; Mathematics
    Abstract. Weconsiderevolutionsforamaterialmodelwhichcouplesscalardamage with strain gradient plasticity, in small strain assumptions. For strain gradient plasticity, we follow the Gurtin-Anand formulation [Gurtin-Anand 2005]. The aim of the present model is to account for different phenomena: on the one hand the elastic stiffness reduces and the plastic yield surface shrinks due to material’s degradation, on the other hand the dislocation density affects the damage growth. The main result of this paper is the existence of a globally stable quasistatic evolution (in the so- called energetic formulation). Furthermore we study the limit model as the strain gradient terms tend to zero. Under stronger regularity assumptions, we show that the evolutions converge to the ones for the coupled elastoplastic–damage model studied in [Crismale, 2014].
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    Globally stable quasistatic evolution for a coupled elastoplastic-damage model
    (SISSA, 2014) Crismale, Vito; Mathematics
    We show the existence of globally stable quasistatic evolutions for a material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage a ects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.
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    Quasistatic crack growth based on viscous approximation: a model with branching and kinking
    (2016) Crismale, Vito; Lazzaroni, Giuliano; Mathematics
    Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.
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    Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model
    (SISSA, 2015) Crismale, Vito; Lazzaroni, Giuliano
    Employing the technique of vanishing viscosity and time rescaling, we show the exis- tence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions.