Browsing by Author "Riva, Filippo"

Now showing 1 - 5 of 5
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    A continuous dependence result for a dynamic debonding model in dimension one
    (SISSA, 2019-03-07) Riva, Filippo; Mathematics
    In this paper we address the problem of continuous dependence on initial and boundary data for a one-dimensional debonding model describing a thin film peeled away from a substrate. The system underlying the process couples the weakly damped wave equation with a Griffith’s criterion which rules the evolution of the debonded region. We show that under general convergence assumptions on the data the corresponding solutions converge to the limit one with respect to different natural topologies.
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    Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping
    (2018-07-16) Riva, Filippo; Nardini, Lorenzo; Mathematics
    In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.
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    On a Phase-field model of damage for hybrid laminates with cohesive interfaces
    (SISSA, 2020-07-17) Bonetti, Elena; Cavaterra, Cecilia; Freddi, Francesco; Riva, Filippo
    In this paper we investigate a rate{independent model for hybrid laminates described by a damage phase field approach on two layers coupled with a cohesive law governing the behaviour of their interface. For the analysis we adopt the notion of energetic evolution, based on global minimisation of the involved energy. Due to the presence of the cohesive zone, as already emerged in literature, compactness mathematical issues lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement discontinuity reached during the evolution. A new strategy which allows to recover the equivalence between the fictitious and the real variable under general loading-unloading regimes is illustrated. The argument is based on temporal regularity of energetic evolutions. This regularity is achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.
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    On the approximation of quasistatic evolutions for the debonding of a thin film viavanishing inertia and viscosity
    (2019-06-24) Riva, Filippo
    In this paper we contribute to studying the issue of quasistatic limit in the context of Griffith’s theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking friction into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.
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    A Vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers
    (SISSA, 2020-07-21) Gidoni, Paolo; Riva, Filippo
    We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical solutions to the quasistatic one, employing the concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.