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In this paper we contribute to studying the issue of quasistatic limit in thecontext of Griffith's theory by investigating a one-dimensional debondingmodel. It describes the evolution of a thin film partially glued to a rigidsubstrate and subjected to a vertical loading. Taking friction into account andunder suitable assumptions on the toughness of the glue, we prove that, incontrast to what happens in the undamped case, dynamic solutions converge tothe quasistatic one when inertia and viscosity go to zero, except for apossible discontinuity at the initial time. We then characterise the size ofthe jump by means of an asymptotic analysis of the debonding front.

On the approximation of quasistatic evolutions for the debonding of a thin film via vanishing inertia and viscosity