01047nas a2200133 4500008004100000245007000041210006900111300001400180490000700194520062800201100002400829700002100853856003900874 2018 eng d00aAnalysis of a Dynamic Peeling Test with Speed-Dependent Toughness0 aAnalysis of a Dynamic Peeling Test with SpeedDependent Toughness a1206-12270 v783 a
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'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.
1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1137/17M114735400945nas a2200109 4500008004100000245010200041210006900143520053000212100002100742700001800763856005400781 2018 en d00aExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping0 aExistence and uniqueness of dynamic evolutions for a one dimensi3 aIn 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.
1 aNardini, Lorenzo1 aRiva, Filippo uhttp://preprints.sissa.it/xmlui/handle/1963/3531901019nas a2200157 4500008004100000022001400041245008700055210006900142260000800211300001400219490000700233520053000240100002400770700002100794856004600815 2018 eng d a1432-146700aOn the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One0 aQuasistatic Limit of Dynamic Evolutions for a Peeling Test in Di cFeb a269–3040 v283 aThe 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'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's (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.
1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1007/s00332-017-9407-000999nas a2200121 4500008004100000245009100041210006900132260001000201520057300211100002400784700002100808856004800829 2017 en d00aOn the 1D wave equation in time-dependent domains and the problem of debond initiation0 a1D wave equation in timedependent domains and the problem of deb bSISSA3 aMotivated 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.
1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://preprints.sissa.it/handle/1963/3530200446nas a2200133 4500008004100000022001400041245009200055210006900147260000800216300001400224490000700238100002100245856004600266 2017 eng d a1572-922200aA Note on the Convergence of Singularly Perturbed Second Order Potential-Type Equations0 aNote on the Convergence of Singularly Perturbed Second Order Pot cJun a783–7970 v291 aNardini, Lorenzo uhttps://doi.org/10.1007/s10884-015-9461-y01120nas a2200229 4500008004100000022001400041245008700055210006900142300001600211490000800227520034000235653002200575653003200597653002100629653002500650653003400675653004400709100002100753700002400774700002100798856007100819 2016 eng d a0022-039600aExistence and uniqueness of dynamic evolutions for a peeling test in dimension one0 aExistence and uniqueness of dynamic evolutions for a peeling tes a4897 - 49230 v2613 aIn 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.
10aDynamic debonding10aDynamic energy release rate10aDynamic fracture10aGriffith's criterion10aMaximum dissipation principle10aWave equation in time-dependent domains1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://www.sciencedirect.com/science/article/pii/S0022039616301772