In the theory of linearly elastic fracture mechanics onedimensional 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 timedependent 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.
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On the quasistatic limit for a debonding model in dimension one; a vanishing inertia and viscosity approach
Research Group:
Filippo Riva
Institution:
SISSA
Location:
A133
Schedule:
Thursday, May 23, 2019  10:00
Abstract:
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