Calculus of Variations and Geometric Measure Theory

R. Scala

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

created by scala on 15 May 2014
modified on 28 Jan 2016



Inserted: 15 may 2014
Last Updated: 28 jan 2016

Year: 2014


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 behaviour 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 that satisfies an energy inequality and a semistability condition at all times. In the one-dimensional case we give a more detailed description of the possible features of such limit evolutions and we show that they behaves very similar to the limit of the solutions of the dynamic model where no viscosity in the adhesive is taken into account.

Keywords: Variational methods, quasistatic evolution, vanishing viscosity, delamination, iperbolic PDEs, non linear equations