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.

Accepted:

DOI: 10.1051/cocv/2016006

Keywords: Visco-elasticity, delamination, contact mechanics, vanishing viscosity, hyperbolic PDEs systems

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@article{COCV_2017__23_2_593_0, author = {Scala, Riccardo}, title = {Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {593--625}, publisher = {EDP-Sciences}, volume = {23}, number = {2}, year = {2017}, doi = {10.1051/cocv/2016006}, mrnumber = {3608095}, zbl = {1397.35306}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016006/} }

TY - JOUR AU - Scala, Riccardo TI - Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 593 EP - 625 VL - 23 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016006/ DO - 10.1051/cocv/2016006 LA - en ID - COCV_2017__23_2_593_0 ER -

%0 Journal Article %A Scala, Riccardo %T Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 593-625 %V 23 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016006/ %R 10.1051/cocv/2016006 %G en %F COCV_2017__23_2_593_0

Scala, Riccardo. Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 2, pp. 593-625. doi : 10.1051/cocv/2016006. http://archive.numdam.org/articles/10.1051/cocv/2016006/

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