Geodesic
Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish
Scala, Riccardo1
1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 593-625

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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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016006
Classification : 35L04, 74C10, 74H10, 74R99
Keywords: Visco-elasticity, delamination, contact mechanics, vanishing viscosity, hyperbolic PDEs systems

Scala, Riccardo 1

1 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany. 
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     title = {Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish},
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Scala, Riccardo. Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 593-625. doi: 10.1051/cocv/2016006

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