On the approximation of quasistatic evolutions for the debonding of a thin film via vanishing inertia and viscosity. (English) Zbl 1439.35314
Summary: 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 viscosity 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.
MSC:
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 74K35 | Thin films |
| 35R35 | Free boundary problems for PDEs |
| 70F40 | Problems involving a system of particles with friction |
Keywords:
dynamic debonding; quasistatic debonding; Griffith’s criterion; quasistatic limit; vanishing inertia; viscosity limitReferences:
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