@article {doi:10.1137/17M1147354, title = {Analysis of a Dynamic Peeling Test with Speed-Dependent Toughness}, journal = {SIAM Journal on Applied Mathematics}, volume = {78}, number = {2}, year = {2018}, pages = {1206-1227}, abstract = {

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 Griffith{\textquoteright}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.

}, doi = {10.1137/17M1147354}, url = {https://doi.org/10.1137/17M1147354}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {2018, title = {Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping}, number = {SISSA;28/2018/MATE}, year = {2018}, abstract = {

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{\textquoteright}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{\textquoteright}s criterion.

}, url = {http://preprints.sissa.it/xmlui/handle/1963/35319}, author = {Lorenzo Nardini and Filippo Riva} } @article {Lazzaroni2018, title = {On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One}, journal = {Journal of Nonlinear Science}, volume = {28}, number = {1}, year = {2018}, month = {Feb}, pages = {269{\textendash}304}, abstract = {

The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith{\textquoteright}s criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith{\textquoteright}s (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

}, issn = {1432-1467}, doi = {10.1007/s00332-017-9407-0}, url = {https://doi.org/10.1007/s00332-017-9407-0}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {2017, title = {On the 1D wave equation in time-dependent domains and the problem of debond initiation}, number = {SISSA;56/2017/MATE}, year = {2017}, institution = {SISSA}, abstract = {

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.

}, url = {http://preprints.sissa.it/handle/1963/35302}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {Nardini2017, title = {A Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations}, journal = {Journal of Dynamics and Differential Equations}, volume = {29}, number = {2}, year = {2017}, month = {Jun}, pages = {783{\textendash}797}, issn = {1572-9222}, doi = {10.1007/s10884-015-9461-y}, url = {https://doi.org/10.1007/s10884-015-9461-y}, author = {Lorenzo Nardini} } @article {DALMASO20164897, title = {Existence and uniqueness of dynamic evolutions for a peeling test in dimension one}, journal = {Journal of Differential Equations}, volume = {261}, number = {9}, year = {2016}, pages = {4897 - 4923}, abstract = {

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.

}, keywords = {Dynamic debonding, Dynamic energy release rate, Dynamic fracture, Griffith{\textquoteright}s criterion, Maximum dissipation principle, Wave equation in time-dependent domains}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2016.07.012}, url = {http://www.sciencedirect.com/science/article/pii/S0022039616301772}, author = {Gianni Dal Maso and Giuliano Lazzaroni and Lorenzo Nardini} }