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Archive / INF Seminars / INF_2025_05_20_EleonoraMaggiorelli

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	Griffith's criterion for phase-field fracture

Host: Patrick Zulian

Tuesday

20.05

USI Campus EST, Room D0.02

12:45 - 13:30


	Eleonora Maggiorelli Università di Pavia

Abstract: Phase field evolutions are obtained by means of time discrete schemes, providing at each time step an equilibrium configuration of the system, which is usually computed by descent methods for the free energy (e.g. staggered and monolithic schemes) under a suitable irreversibility constraint on the phase-field parameter. We studied in detail the time continuous limits of these evolutions considering monotonicity as irreversibility constraint and providing a general result, which holds independently of the scheme employed in the incremental problem. In particular, we showed that in the steady state regime the limit evolution is simultaneous (in displacement and phase field parameter) and satisfies Griffith’s criterion in terms of toughness and of a phase field energy release rate. In the unsteady regime the limit evolution may instead depend on the adopted scheme and Griffith’s criterion may not hold. Technically, the proof employs a suitable reparametrization of the time discrete points, whose Kuratowski limit characterizes the set of steady state propagation. The study of the quasi-static time continuous limit relies on the strong convergence of the phase field function together with the convergence of the power identity. Moreover, I will present the outcomes of some numerical simulations that endorse our theoretical results. Specifically, we considered two model problems, one for steady and one for unsteady-state crack propagations showing the consistency of the phase-field model with Griffith criterion.

Biography: Eleonora Maggiorelli is a PhD candidate in Computational Mathematics and Decision Sciences, jointly offered by the University of Pavia (Italy) and USI. She earned both her Bachelor's and Master's degrees in Mathematics from the University of Pavia. Her Master's thesis was developed in collaboration with Eni S.p.A., where she completed a one-year internship. Her current research, supervised by Prof. Matteo Negri, focuses on phase-field models for brittle fracture, explored from both theoretical and computational perspectives. Her main theoretical contribution is the study titled “Energy Release and Griffith’s Criterion for Phase-Field Fracture”, which proves that the limit of phase-field evolutions satisfies Griffith’s criterion in terms of a phase-field energy release rate. These theoretical findings are supported by numerical simulations developed using FreeFem++. She spent two months at ETH Zurich as a visiting researcher in Prof. De Lorenzis' group, and she is currently on a research visit at USI, working with Prof. Rolf Krause’s group.