Browsing by Author "Nardini, Lorenzo"

Now showing 1 - 5 of 5
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    Analysis of a dynamic peeling test with speed-dependent toughness
    (2017) Lazzaroni, Giuliano; Nardini, Lorenzo; Mathematics
    We analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffth's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.
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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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    Existence and uniqueness of dynamic evolutions for a peeling test in dimension one
    (SISSA, 2016) Dal Maso, Gianni; Lazzaroni, Giuliano; Nardini, Lorenzo; Mathematics
    In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.
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    On the 1D wave equation in time-dependent domains and the problem of debond initiation
    (SISSA, 2017) Lazzaroni, Giuliano; Nardini, Lorenzo; Mathematics
    Motivated by a debonding model for a thin film peeled from a substrate, we analyse the one-dimensional wave equation, in a time-dependent domain which is degenerate at the initial time. In the first part of the paper we prove existence for the wave equation when the evolution of the domain is given; in the second part of the paper, the evolution of the domain is unknown and is governed by an energy criterion coupled with the wave equation. Our existence result for such coupled problem is a contribution to the study of crack initiation in dynamic fracture.