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Existence of solutions to a phase-field model of dynamic crack propagation

Speaker: 
Maicol Caponi
Institution: 
SISSA
Schedule: 
Friday, April 20, 2018 - 14:00
Location: 
A-133
Abstract: 

In this talk I discuss about mathematical models of dynamic brittle fracture based on Griffith's criterion. In particular I focus on the phase-field ones, which rely on the Ambrosio-Tortorelli approximation. In these models the crack is aprroximated by a function $v \in \left[ 0,1 \right]$ (called phase-field) which takes values close to $0$ in a small neighborhood of the crack set, and values close to $1$ far from it. By adapting a time discretization scheme, I prove the existence of a solution for a phase-field model in which the dissipative effects due to the crack tips speed are taken into account. Finally I show that this evolution satisfies an energy dissipation balance according to Griffith's criterion.

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