Mathematics

In the theory of linearly elastic fracture mechanics one-dimensional  debonding models, or peeling tests, provide a simplified but still  meaningful version of crack growth models based on Griffith's criterion. They are both described by the wave equation in a  time-dependent domain coupled with suitable energy balances and  irreversibility conditions.Unlike the general framework, peeling tests  allow to deal with a natural issue of great interest arising in fracture mechanics. It can  be stated as follows: although all these models are dynamic by nature,  the evolution process is often assumed to be quasistatic (namely the body is at equilibrium at every time) since inertial effects can be  neglected if the speed of external loading is very slow with respect  to the one of internal oscillations. Despite this assumption seems to be reasonable, its mathematical proof is really far from being  achieved.In this talk we validate the quasistatic assumption in a  particular damped debonding model, showing that dynamic evolutions  converge to the quasistatic one as inertia and viscosity go to zero.  We also highlight how the presence of viscosity is crucial to get this  kind of convergence.