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A dynamic model for viscoelastic materials with prescribed growing cracks

Francesco Sapio
Friday, June 14, 2019 - 14:00

In this seminar I consider a class of dynamic viscoelastic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. The system considered is a modification of well known Kelvin-Voigt's model, which is a deformation model and it is not appropriate to describe the crack growth in a viscoelastic material. By requiring some regularity conditions on the viscosity tensor, I first provide an existence result, in which I show that there exists a particular solution obtained thanks to a discretization in time procedure, then I show the validity of an energy-dissipation inequality. Moreover, under stronger assumptions, I prove a uniqueness result in the dimensional case $d=2$. The first step is to prove the theorem in a fixed domain, and then to pass to time-dependent domain. Finally, I exhibit an example of solution, for which the energy-dissipation balance is not satisfied in classic form, but it is valid with an additional dissipation term due to the crack growth. 

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