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Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish

TitleLimit of viscous dynamic processes in delamination as the viscosity and inertia vanish
Publication TypeJournal Article
Year of Publication2017
AuthorsScala, R
JournalESAIM: COCV
Volume23
Pagination593-625
Abstract

We introduce a model of dynamic evolution of a delaminated visco-elastic body with viscous adhesive. We prove the existence of solutions of the corresponding system of PDEs and then study the behavior of such solutions when the data of the problem vary slowly. We prove that a rescaled version of the dynamic evolutions converge to a “local” quasistatic evolution, which is an evolution satisfying an energy inequality and a momentum balance at all times. In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101–126], where no viscosity in the adhesive is taken into account.

URLhttps://doi.org/10.1051/cocv/2016006
DOI10.1051/cocv/2016006

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