[Dottorcomp] Seminari di Matematica Applicata, 03/06/2025, Masato Kimura

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 3 Giugno 2025, alle ore 15 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Masato Kimura (Kanazawa University)

terrà un seminario dal titolo:

Energy-dissipation in irreversible phase field fracture models and their
extensions.

Abstract: This talk presents an overview of the Irreversible Phase Field
Model for Fracture (Irreversible F-PFM) proposed by the speaker and
collaborators, which is based on the concept of irreversible gradient
flows. An irreversible gradient flow is a constrained gradient flow in which
monotonicity in time is enforced, leading to a natural
energy-dissipation identity [Akagi–Kimura, 2019; Kimura–Negri, 2021].

The Irreversible F-PFM applies this framework to the Ambrosio–Tortorelli
regularization of the variational fracture model by Francfort and
Marigo, ensuring both the irreversibility of crack evolution and
monotonic energy decay (i.e., a consistent dissipation structure). This
model is compactly formulated using partial differential equations and
is readily amenable to standard finite element solvers, enabling crack
propagation simulations without a priori knowledge of the crack path.

After reviewing the mathematical structure of the Irreversible F-PFM,
the talk will introduce a range of recent extensions and their finite
element simulations, each highlighting how the dissipation structure is
preserved or adapted. These include: Irreversible F-PFM under unilateral
constraints; Thermo-mechanical fracture models; Phase field modeling of
fracking in oil and gas reservoirs; Desiccation-induced fracture
modeling; Dynamic phase-field fracture models and seismic fault rupture.
Through these examples, we aim to highlight the versatility and
robustness of the irreversible phase-field approach in simulating
complex fracture phenomena across disciplines.
-----------------------------------------
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/